The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics.The discoveries of nontrivial topological phases in real materials provide a series of arc...The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics.The discoveries of nontrivial topological phases in real materials provide a series of archetype materials to further explore the topological physics.展开更多
In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequal...In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.展开更多
In this paper, we prove the existence of at least one positive solution pair （u, v）∈ H1（RN） × H1（RN） to the following semilinear elliptic system {-△u＋u=f（x,v）,x∈RN,-△u＋u=g（x,v）,x∈RN （0.1）,by us...In this paper, we prove the existence of at least one positive solution pair （u, v）∈ H1（RN） × H1（RN） to the following semilinear elliptic system {-△u＋u=f（x,v）,x∈RN,-△u＋u=g（x,v）,x∈RN （0.1）,by using a linking theorem and the concentration-compactness principle. The main conditions we imposed on the nonnegative functions f, g ∈C0（RN× R1） are that, f（x, t） and g（x, t） are superlinear at t = 0 as well as at t =＋∞, that f and g are subcritical in t and satisfy a kind of monotonic conditions. We mention that we do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as an extension to a recent result of Miyagaki and Souto [J. Diff. Equ. 245（2008）, 3628-3638] concerning the existence of a positive solution to the semilinear elliptic boundary value problem {-△u＋u=f（x,u）,x∈Ω,u∈H0^1（Ω） where Ω ∩→RN is bounded and a result of Li and Yang [G. Li and J. Yang： Communications in P.D.E. Vol. 29（2004） Nos.5＆ 6.pp.925-954, 2004] concerning （0.1） when f and g are asymptotically linear.展开更多
Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.
In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in R^N which includes the so-called modified nonlinear Schrodinger equation as a special case. Combining the dual ap...In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in R^N which includes the so-called modified nonlinear Schrodinger equation as a special case. Combining the dual approach and the nonsmooth critical point theory, we obtain the existence of a nontrivial solution.展开更多
Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegati...Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.展开更多
In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivia...In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.展开更多
In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-comp...In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem展开更多
In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous ...In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.展开更多
Quantum phase transition in topological insulators has drawn heightened attention in condensed matter physics and future device applications. Here we report the magnetotransport properties of single crystalline （Bi0....Quantum phase transition in topological insulators has drawn heightened attention in condensed matter physics and future device applications. Here we report the magnetotransport properties of single crystalline （Bi0.92In0.08）2Se3. The average mobility of^1000 cm2·V-1·s-1 is obtained from the Lorentz law at the low field （〈 3 T） up to 50 K. The quantum oscillations rise at a field of^5 T, revealing a high mobility of^1.4×104 cm2·V-1·s-1 at 2 K. The Dirac surface state is evident by the nontrivial Berry phase in the Landau-Fan diagram. The properties make the （Bi0.92In0.08）2Se3 a promising platform for the investigation of quantum phase transition in topological insulators.展开更多
Compounds with the A15 structure have attracted extensive attention due to their superconductivity and nontrivial topological band structures.We have successfully grown Nb_(3)Sb single crystals with the A15 structure ...Compounds with the A15 structure have attracted extensive attention due to their superconductivity and nontrivial topological band structures.We have successfully grown Nb_(3)Sb single crystals with the A15 structure and systematically measured the longitudinal resistivity,Hall resistivity and quantum oscillations in magnetization.Similar to other topological trivial/nontrivial semimetals,Nb_(3)Sb exhibits large magnetoresistance(MR)at low temperatures(717%,2 K and 9 T),unsaturating quadratic field dependence of MR and up-turn behavior in ρ_(xx)(T)curves under magnetic field,which is considered to result from a perfect hole-electron compensation,as evidenced by the Hall resistivity measurements.The nonzero Berry phase obtained from the de-Hass van Alphen(dHvA)oscillations demonstrates that Nb_(3)Sb is topologically nontrivial.These results indicate that Nb_(3)Sb superconductor is also a semimetal with large MR and nontrivial Berry phase.This indicates that Nb_(3)Sb may be another platform to search for the Majorana zero-energy mode.展开更多
We report the nontrivial topological states in an intrinsic type-Ⅱ superconductor BaSn_(5)(T_(c)∼4.4 K)probed by measuring the magnetization,specific heat,de Haas–van Alphen(dHvA)effect,and by performing first-prin...We report the nontrivial topological states in an intrinsic type-Ⅱ superconductor BaSn_(5)(T_(c)∼4.4 K)probed by measuring the magnetization,specific heat,de Haas–van Alphen(dHvA)effect,and by performing first-principles calculations.The first-principles calculations reveal a topological nodal ring structure centered at the H point in the k_(z)=πplane of the Brillouin zone,which could be gapped by spin-orbit coupling(SOC),yielding relatively small gaps below and above the Fermi level of about 0.04 eV and 0.14 eV,respectively.The SOC also results in a pair of Dirac points along theΓ–A direction,located at∼0.2 eV above the Fermi level.The analysis of the dHvA quantum oscillations supports the calculations by revealing a nontrivial Berry phase originating from the hole and electron pockets related to the bands forming the Dirac cones.Thus,our study provides an excellent avenue for investigating the interplay between superconductivity and nontrivial topological states.展开更多
Some new results on the existence of nonnegative nontrivial solutions of the nonlinear Volterra integral equation,u(x)= k(x,s)g(u(s))ds,(x≥0),are given and their applications are shown.
Materials featuring topological energy bands and nontrivial surface states hold significant promise in unlocking unprecedented opportunities for innovating electrocatalytic mechanism.However,it remains a challenge to ...Materials featuring topological energy bands and nontrivial surface states hold significant promise in unlocking unprecedented opportunities for innovating electrocatalytic mechanism.However,it remains a challenge to realize superior topological catalysts which can carry both high catalytic activity and excellent catalytic stability.Here,we propose that a family of Ni-based binary materials hosting fantasying topological conjunct-nodalpoint state and a large nontrivial energy window(NEWD)represents an ideal choice for such superior topological catalysts in hydrogen evolution reaction.The presence of conjunct-nodal-points ensures long Fermi arcs on the surface,thereby enabling an extremely high catalytic activity.The NEWD plays a crucial role in stabilizing the high catalytic activity against external perturbations,such as strain and electron/hole injection.The roles for conjunctnodal-points and NEWD are substantiated by the observable weakening of catalytic performance during topological phase transitions,which result in the removal of the conjunct-nodal-points,NEWD and their corresponding long Fermi arcs.Our work unveils a hidden mechanism and opens a feasible route for developing superior quantum catalysts from novel topology point of view.展开更多
In this work,we use the variant fountain theorem to study the existence of nontrivial solutions for the superquadratic fractional difference boundary value problem:{T△^(v)_(t-1)(t△^(v)_(v-1)x(t))=f(x(t+v-1)),t∈[0,T...In this work,we use the variant fountain theorem to study the existence of nontrivial solutions for the superquadratic fractional difference boundary value problem:{T△^(v)_(t-1)(t△^(v)_(v-1)x(t))=f(x(t+v-1)),t∈[0,T]N_(0),x(v-2)=[tΔ^(v)_(v-1)x(t)]_(t=T=0.The existence of nontrivial solutions is obtained in the case of super quadratic growth of the nonlinear term f by change of fountain theorem.展开更多
In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B...In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B（t） is a semipositive symmetric continuous matrix and ^H（t, z） = satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.展开更多
This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),...This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),y(t-1)).)Some new existence criteria are obtained.展开更多
The singular boundary value problems for fourth-order differential equations are considered under some conditions concerning the first eigenvalues of the relevant linear operators. Sufficient conditions which guarante...The singular boundary value problems for fourth-order differential equations are considered under some conditions concerning the first eigenvalues of the relevant linear operators. Sufficient conditions which guarantee the existence of nontrivial solutions are obtained. We use the topological degree to prove our main results.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12374159 and 11974076)the Key Project of Natural Science Foundation of Fujian Province,China(Grant No.2021J02012)+1 种基金the GHfund A(Grant No.202302019222)the Research Foundation of the Academy of Carbon Neutrality of Fujian Normal University,China(Grant No.TZH2022-05)。
文摘The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics.The discoveries of nontrivial topological phases in real materials provide a series of archetype materials to further explore the topological physics.
基金Supported by NSFC(10471047)NSF Guangdong Province(05300159).
文摘In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.
基金supported by NSFC (10571069, 10631030) and Hubei Key Laboratory of Mathematical Sciencessupported by the fund of CCNU for PHD students(2009019)
文摘In this paper, we prove the existence of at least one positive solution pair （u, v）∈ H1（RN） × H1（RN） to the following semilinear elliptic system {-△u＋u=f（x,v）,x∈RN,-△u＋u=g（x,v）,x∈RN （0.1）,by using a linking theorem and the concentration-compactness principle. The main conditions we imposed on the nonnegative functions f, g ∈C0（RN× R1） are that, f（x, t） and g（x, t） are superlinear at t = 0 as well as at t =＋∞, that f and g are subcritical in t and satisfy a kind of monotonic conditions. We mention that we do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as an extension to a recent result of Miyagaki and Souto [J. Diff. Equ. 245（2008）, 3628-3638] concerning the existence of a positive solution to the semilinear elliptic boundary value problem {-△u＋u=f（x,u）,x∈Ω,u∈H0^1（Ω） where Ω ∩→RN is bounded and a result of Li and Yang [G. Li and J. Yang： Communications in P.D.E. Vol. 29（2004） Nos.5＆ 6.pp.925-954, 2004] concerning （0.1） when f and g are asymptotically linear.
基金supported by the National Natural Science Foundation of China and 973 Program of STM.
文摘Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.
基金supported partially by National Natural Science Foundation of China(11771385,11661083)the Youth Foundation of Yunnan Minzu University(2017QNo3)
文摘In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in R^N which includes the so-called modified nonlinear Schrodinger equation as a special case. Combining the dual approach and the nonsmooth critical point theory, we obtain the existence of a nontrivial solution.
文摘Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.
基金This work was supported by Key Academic Discipline of Zhejiang Province of China(2005)the Natural Science Foundation of Zhejiang Province of China(Y605144)the Education Department of Zhejiang Province of China(20051897).
文摘In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.
文摘In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem
基金supported by the National Natural Science Foundation of China(11326139,11326145)Tian Yuan Foundation(KJLD12067)+1 种基金Central Specialized Fundation of SCUEC(CZQ13013)the Project of Jiangxi Province Technology Hall(2014BAB211010)
文摘In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.
基金Project supported by the National Key Basic Research Program of China(Grant Nos.2014CB921103 and 2017YFA0206304)the National Natural Science Foundation of China(Grant Nos.U1732159 and 11274003)Collaborative Innovation Center of Solid-State Lighting and Energy-Saving Electronics,China
文摘Quantum phase transition in topological insulators has drawn heightened attention in condensed matter physics and future device applications. Here we report the magnetotransport properties of single crystalline （Bi0.92In0.08）2Se3. The average mobility of^1000 cm2·V-1·s-1 is obtained from the Lorentz law at the low field （〈 3 T） up to 50 K. The quantum oscillations rise at a field of^5 T, revealing a high mobility of^1.4×104 cm2·V-1·s-1 at 2 K. The Dirac surface state is evident by the nontrivial Berry phase in the Landau-Fan diagram. The properties make the （Bi0.92In0.08）2Se3 a promising platform for the investigation of quantum phase transition in topological insulators.
基金the National Key R&D Program of China(Grant No.2016YFA0300402)the National Natural Science Foundation of China(Grant Nos.12074335,and 11974095)the Fundamental Research Funds for the Central Universities。
文摘Compounds with the A15 structure have attracted extensive attention due to their superconductivity and nontrivial topological band structures.We have successfully grown Nb_(3)Sb single crystals with the A15 structure and systematically measured the longitudinal resistivity,Hall resistivity and quantum oscillations in magnetization.Similar to other topological trivial/nontrivial semimetals,Nb_(3)Sb exhibits large magnetoresistance(MR)at low temperatures(717%,2 K and 9 T),unsaturating quadratic field dependence of MR and up-turn behavior in ρ_(xx)(T)curves under magnetic field,which is considered to result from a perfect hole-electron compensation,as evidenced by the Hall resistivity measurements.The nonzero Berry phase obtained from the de-Hass van Alphen(dHvA)oscillations demonstrates that Nb_(3)Sb is topologically nontrivial.These results indicate that Nb_(3)Sb superconductor is also a semimetal with large MR and nontrivial Berry phase.This indicates that Nb_(3)Sb may be another platform to search for the Majorana zero-energy mode.
基金supported by the National Natural Science Foundation of China (Grant Nos. 92065201, 11774223, and U2032213)the Open Project of Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education)+3 种基金Shanghai Jiao Tong University (Grant No. 2020–04)supported by the Shenzhen Peacock Team Plan (Grant No. KQTD20170809110344233)Bureau of Industry and Information Technology of Shenzhen through the Graphene Manufacturing Innovation Center (Grant No. 201901161514)support from Analytical Instrumentation Center, SPST, Shanghai Tech University (Grant No. SPST-AIC10112914)
文摘We report the nontrivial topological states in an intrinsic type-Ⅱ superconductor BaSn_(5)(T_(c)∼4.4 K)probed by measuring the magnetization,specific heat,de Haas–van Alphen(dHvA)effect,and by performing first-principles calculations.The first-principles calculations reveal a topological nodal ring structure centered at the H point in the k_(z)=πplane of the Brillouin zone,which could be gapped by spin-orbit coupling(SOC),yielding relatively small gaps below and above the Fermi level of about 0.04 eV and 0.14 eV,respectively.The SOC also results in a pair of Dirac points along theΓ–A direction,located at∼0.2 eV above the Fermi level.The analysis of the dHvA quantum oscillations supports the calculations by revealing a nontrivial Berry phase originating from the hole and electron pockets related to the bands forming the Dirac cones.Thus,our study provides an excellent avenue for investigating the interplay between superconductivity and nontrivial topological states.
文摘Some new results on the existence of nonnegative nontrivial solutions of the nonlinear Volterra integral equation,u(x)= k(x,s)g(u(s))ds,(x≥0),are given and their applications are shown.
基金This work is supported by the Youth Foundation, NSFC.
文摘In this paper, we get the existence result of the nontrivial weak solution (λ, u) of the following eigenvalue problem with natural growth conditions.
基金financially supported by the National Natural Science Foundation of China(No.12274112)funded by the Overseas Scientists Sponsorship Program of Hebei Province(No.C20210330)+1 种基金the State Key Laboratory of Reliability and Intelligence of Electrical Equipment of Hebei University of Technology(No.EERI_PI2020009)S&T Program of Hebei(No.225676163GH)。
文摘Materials featuring topological energy bands and nontrivial surface states hold significant promise in unlocking unprecedented opportunities for innovating electrocatalytic mechanism.However,it remains a challenge to realize superior topological catalysts which can carry both high catalytic activity and excellent catalytic stability.Here,we propose that a family of Ni-based binary materials hosting fantasying topological conjunct-nodalpoint state and a large nontrivial energy window(NEWD)represents an ideal choice for such superior topological catalysts in hydrogen evolution reaction.The presence of conjunct-nodal-points ensures long Fermi arcs on the surface,thereby enabling an extremely high catalytic activity.The NEWD plays a crucial role in stabilizing the high catalytic activity against external perturbations,such as strain and electron/hole injection.The roles for conjunctnodal-points and NEWD are substantiated by the observable weakening of catalytic performance during topological phase transitions,which result in the removal of the conjunct-nodal-points,NEWD and their corresponding long Fermi arcs.Our work unveils a hidden mechanism and opens a feasible route for developing superior quantum catalysts from novel topology point of view.
文摘In this work,we use the variant fountain theorem to study the existence of nontrivial solutions for the superquadratic fractional difference boundary value problem:{T△^(v)_(t-1)(t△^(v)_(v-1)x(t))=f(x(t+v-1)),t∈[0,T]N_(0),x(v-2)=[tΔ^(v)_(v-1)x(t)]_(t=T=0.The existence of nontrivial solutions is obtained in the case of super quadratic growth of the nonlinear term f by change of fountain theorem.
基金supported by the National Natural Science Foundation of China (Nos. 10531050, 10621101)the 973 Project of the Ministry of Science and Technology of China.
文摘In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B（t） is a semipositive symmetric continuous matrix and ^H（t, z） = satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.
基金Sapported by the National Science Foundation of China.
文摘This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),y(t-1)).)Some new existence criteria are obtained.
基金the National Natural Science Foundation of China (10671167).
文摘The singular boundary value problems for fourth-order differential equations are considered under some conditions concerning the first eigenvalues of the relevant linear operators. Sufficient conditions which guarantee the existence of nontrivial solutions are obtained. We use the topological degree to prove our main results.
