In this paper, we determine the infimum and the supremum of the Dirich-let eigenvalues λn(p) (n = 1,2,…)of the problem t∈ ?[0,T], where 1 < p < ∞, and the weights p are nonnegative and are subject to conditi...In this paper, we determine the infimum and the supremum of the Dirich-let eigenvalues λn(p) (n = 1,2,…)of the problem t∈ ?[0,T], where 1 < p < ∞, and the weights p are nonnegative and are subject to conditions p(t)dt = M and max(e[0,T] p(t) = H. It is also explained for whatweights p the infimum and the supremum will be attained.展开更多
In this paper, we propose that the Green functions are benefit to obtainingthe necessary estimates in the applications of Leray-Schauder degree to boundaryvalue problems of nonlinear differential equations. As an exam...In this paper, we propose that the Green functions are benefit to obtainingthe necessary estimates in the applications of Leray-Schauder degree to boundaryvalue problems of nonlinear differential equations. As an example, a three pointboundary value problem of second order differential equations is considered inthis paper and all of the results obtained by the Wirtinger type inequalities anddifferential inclusions in Gupta [5] and Marano [11] will be improved.展开更多
In this letter applying the results about structural stabilities （cf. R. Maé & C. Pugh, Dynamical Systems-Warwick 1974, Lecture Notes Math., Vol. 468）, we study the π<sub>1</sub> property of An...In this letter applying the results about structural stabilities （cf. R. Maé & C. Pugh, Dynamical Systems-Warwick 1974, Lecture Notes Math., Vol. 468）, we study the π<sub>1</sub> property of Anosov endomorphisms on tori. We have proved the展开更多
This paper considers the following question: Given an Anosov endomorphism f on T^m, whether f is topologically conjugate to some hyperbolic total endomorphism? It is well known that the answer for Anosov diffeomorphis...This paper considers the following question: Given an Anosov endomorphism f on T^m, whether f is topologically conjugate to some hyperbolic total endomorphism? It is well known that the answer for Anosov diffeomorphisms and expanding endomorphisms is affirmative. Hwever for the remainder Anosov endomorphisms, a quite different answer is obtained in this paper, i. e., for generic Anosov endomorphisms, they are not topologically conjugate to any hyperbolic toral endomorphism.展开更多
This note will give some classification results for local and global C^1 diffeomorphisms of R under C^1 conjugacy. For γ=1, 2,…, ∞, ω, let D~γ(0)={f: R→R is C~γ; f’(x)】0, x∈R; and f has 0 asits unique fixed ...This note will give some classification results for local and global C^1 diffeomorphisms of R under C^1 conjugacy. For γ=1, 2,…, ∞, ω, let D~γ(0)={f: R→R is C~γ; f’(x)】0, x∈R; and f has 0 asits unique fixed point} (local diffeomorphisms of R). In Refs. [1] and [2], we have considered the existence of smooth embedding flows and the other related problems for f∈D~γ(0). As a result, we prove that the following classifications have some numerical invariants展开更多
Rotation numbers are used in this paper to study the periodic and anti-periodic eigenvalues of the one-dimensional p-Laplacian with a periodic weight which changes sign. The analysis proves that for any nonnegative i...Rotation numbers are used in this paper to study the periodic and anti-periodic eigenvalues of the one-dimensional p-Laplacian with a periodic weight which changes sign. The analysis proves that for any nonnegative integer n, ρ -1(n/2) is the union of two closed intervals, one of which lies in [FK(W+3mm?3mm][TPP533A,+3mm?2mm] + and the other in [FK(W+3mm?3mm][TPP533A,+3mm?2mm] -, and the endpoints of these intervals yield the corresponding periodic and anti-periodic eigenvalues.展开更多
Embedding flows are used to obtain a rigidity result on strongly topological conjugacy of families of diffeomorphisms,i.e.families of C4(2≤r≤∞) diffeomorphisms,the strongly topologically conjugating homeomor-phisms...Embedding flows are used to obtain a rigidity result on strongly topological conjugacy of families of diffeomorphisms,i.e.families of C4(2≤r≤∞) diffeomorphisms,the strongly topologically conjugating homeomor-phisms near degenerate saddle-nodes will be differentiable on center manifolds of the saddle-nodes.展开更多
基金Project Supported by the National 973 Project(G1999075100)of Chinathe ExcellentPersonnel Supporting Plan of the Ministry of Education of China.
文摘In this paper, we determine the infimum and the supremum of the Dirich-let eigenvalues λn(p) (n = 1,2,…)of the problem t∈ ?[0,T], where 1 < p < ∞, and the weights p are nonnegative and are subject to conditions p(t)dt = M and max(e[0,T] p(t) = H. It is also explained for whatweights p the infimum and the supremum will be attained.
文摘In this paper, we propose that the Green functions are benefit to obtainingthe necessary estimates in the applications of Leray-Schauder degree to boundaryvalue problems of nonlinear differential equations. As an example, a three pointboundary value problem of second order differential equations is considered inthis paper and all of the results obtained by the Wirtinger type inequalities anddifferential inclusions in Gupta [5] and Marano [11] will be improved.
文摘In this letter applying the results about structural stabilities （cf. R. Maé & C. Pugh, Dynamical Systems-Warwick 1974, Lecture Notes Math., Vol. 468）, we study the π<sub>1</sub> property of Anosov endomorphisms on tori. We have proved the
文摘This paper considers the following question: Given an Anosov endomorphism f on T^m, whether f is topologically conjugate to some hyperbolic total endomorphism? It is well known that the answer for Anosov diffeomorphisms and expanding endomorphisms is affirmative. Hwever for the remainder Anosov endomorphisms, a quite different answer is obtained in this paper, i. e., for generic Anosov endomorphisms, they are not topologically conjugate to any hyperbolic toral endomorphism.
基金Project supported by the Natural Science Foundation of Tsinghua University
文摘This note will give some classification results for local and global C^1 diffeomorphisms of R under C^1 conjugacy. For γ=1, 2,…, ∞, ω, let D~γ(0)={f: R→R is C~γ; f’(x)】0, x∈R; and f has 0 asits unique fixed point} (local diffeomorphisms of R). In Refs. [1] and [2], we have considered the existence of smooth embedding flows and the other related problems for f∈D~γ(0). As a result, we prove that the following classifications have some numerical invariants
基金Supported by the National Basic Research PrioritiesProgram me of China (No.G19990 75 10 8) and theTRAPOYT of the Ministry of Education of China
文摘Rotation numbers are used in this paper to study the periodic and anti-periodic eigenvalues of the one-dimensional p-Laplacian with a periodic weight which changes sign. The analysis proves that for any nonnegative integer n, ρ -1(n/2) is the union of two closed intervals, one of which lies in [FK(W+3mm?3mm][TPP533A,+3mm?2mm] + and the other in [FK(W+3mm?3mm][TPP533A,+3mm?2mm] -, and the endpoints of these intervals yield the corresponding periodic and anti-periodic eigenvalues.
基金Project supported by the National Natural Science Foundation of China and the Basic Science Research Foundation of Tsinghua University.
文摘Embedding flows are used to obtain a rigidity result on strongly topological conjugacy of families of diffeomorphisms,i.e.families of C4(2≤r≤∞) diffeomorphisms,the strongly topologically conjugating homeomor-phisms near degenerate saddle-nodes will be differentiable on center manifolds of the saddle-nodes.
