This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
In this paper, we investigate the existence of positive solutions for a singular third-order three-point boundary value problem with a parameter. By using fixed point index theory, some existence, multiplicity and non...In this paper, we investigate the existence of positive solutions for a singular third-order three-point boundary value problem with a parameter. By using fixed point index theory, some existence, multiplicity and nonexistence results for positive solutions are derived in terms of different values of λ.展开更多
In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP:<br /> <p> <img src="Edit_4da56369-d8f9-42d0-9650-c15af375d30c.bmp" alt="" />, whe...In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP:<br /> <p> <img src="Edit_4da56369-d8f9-42d0-9650-c15af375d30c.bmp" alt="" />, where Δ<em>u</em> = <em>div</em> (<span style="white-space:nowrap;">∇</span><em>u</em>) and Δ<em>v</em> = <em>div</em> (<span style="white-space:nowrap;">∇</span><em>v</em>) are the Laplacian of <em>u</em>, <span style="white-space:nowrap;"><em>λ</em> </span>is a positive parameter, Ω = {<em>x</em> ∈ R<sup><em>n</em></sup> : <em>N</em> > 2, |<em>x</em>| > <em>r</em><sub>0</sub>, <em>r</em><sub>0</sub> > 0}, let <em>i</em> = [1,2] then <em>K<sub>i</sub></em> :[<em>r</em><sub>0</sub>,∞] → (0,∞) is a continuous function such that lim<sub><em>r</em>→∞</sub> <em>k<sub>i</sub></em>(<em>r</em>) = 0 and <img src="Edit_19f045da-988f-43e9-b1bc-6517f5734f9c.bmp" alt="" /> is The external natural derivative, and <img src="Edit_3b36ed6b-e780-46de-925e-e3cf7c6a125f.bmp" alt="" />: [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of <em>f </em>with a) <em>f<sub>i </sub></em>> 0, b) <em>f<sub>i </sub></em>< 0, and c) <em>f<sub>i </sub></em>= 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings. </p>展开更多
In this article, we establish the existence of positive solution for the following Hadamard fractional singular boundary value problem where is continuous and singular at t = a, t = b and x = 0. Further, is Hada...In this article, we establish the existence of positive solution for the following Hadamard fractional singular boundary value problem where is continuous and singular at t = a, t = b and x = 0. Further, is Hadamard fractional derivative of order μ. Moreover, the existence of positive solution has been established using fixed point index for a completely continuous map in a cone. Also, an example is included to show the validity of our result.展开更多
Using the fixed point index in cones, we study the existence of one and two positive solutions to singular second order Neumann boundary value problems under some conditions, which concerns the first eigenvalue of the...Using the fixed point index in cones, we study the existence of one and two positive solutions to singular second order Neumann boundary value problems under some conditions, which concerns the first eigenvalue of the relevant linear problem. Our results improve and extend some known ones in the previous literature.展开更多
In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential eq...In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.展开更多
In this paper, we study a class of fourth-order Neumann boundary value problem (NBVP for short). By virtue of fixed point index and the spectral theory of linear operators, the existence of positive solutions is obtai...In this paper, we study a class of fourth-order Neumann boundary value problem (NBVP for short). By virtue of fixed point index and the spectral theory of linear operators, the existence of positive solutions is obtained under the assumption that the nonlinearity satisfies sublinear or superlinear conditions, which are relevant to the first eigenvalue of the corresponding linear operator.展开更多
In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and l...In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.展开更多
In this paper, we study two kinds of first-order singular discrete systems.By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.
By virtue of the fixed point indices, we discuss the existence of the multiple positive periodic solutions to singular differential equation with state-dependent delay under the conditions concerning the first eigenva...By virtue of the fixed point indices, we discuss the existence of the multiple positive periodic solutions to singular differential equation with state-dependent delay under the conditions concerning the first eigenvalue of the relevant linear operator. The results in this paper are optimal and totally generalize many present results.展开更多
This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space...This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].展开更多
The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t...The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.展开更多
By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary va...By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem, where the nonlinear term is allowed to be nonnegative and unbounded.展开更多
In this paper, we use cone theory and a new method of computation of fixed point index to study a system of nonlinear Hammerstein type integral equations, and the existence of multiple positive solutions to the system...In this paper, we use cone theory and a new method of computation of fixed point index to study a system of nonlinear Hammerstein type integral equations, and the existence of multiple positive solutions to the system is discussed.展开更多
This paper investigates the existence of positive solutions to systems of second order nonlocal boundary value problems with first order derivatives, in which the nonlinear term is not required to be continuous and in...This paper investigates the existence of positive solutions to systems of second order nonlocal boundary value problems with first order derivatives, in which the nonlinear term is not required to be continuous and involves first order derivatives. The main tool used in this paper is a fixed point index theory in a cone.展开更多
This paper deals with the existence of positive solutions to the singular secondorder periodic boundary value problem. We obtain the existence results of positive solutions by the fixed point index theory. The results...This paper deals with the existence of positive solutions to the singular secondorder periodic boundary value problem. We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.展开更多
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘In this paper, we investigate the existence of positive solutions for a singular third-order three-point boundary value problem with a parameter. By using fixed point index theory, some existence, multiplicity and nonexistence results for positive solutions are derived in terms of different values of λ.
文摘In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP:<br /> <p> <img src="Edit_4da56369-d8f9-42d0-9650-c15af375d30c.bmp" alt="" />, where Δ<em>u</em> = <em>div</em> (<span style="white-space:nowrap;">∇</span><em>u</em>) and Δ<em>v</em> = <em>div</em> (<span style="white-space:nowrap;">∇</span><em>v</em>) are the Laplacian of <em>u</em>, <span style="white-space:nowrap;"><em>λ</em> </span>is a positive parameter, Ω = {<em>x</em> ∈ R<sup><em>n</em></sup> : <em>N</em> > 2, |<em>x</em>| > <em>r</em><sub>0</sub>, <em>r</em><sub>0</sub> > 0}, let <em>i</em> = [1,2] then <em>K<sub>i</sub></em> :[<em>r</em><sub>0</sub>,∞] → (0,∞) is a continuous function such that lim<sub><em>r</em>→∞</sub> <em>k<sub>i</sub></em>(<em>r</em>) = 0 and <img src="Edit_19f045da-988f-43e9-b1bc-6517f5734f9c.bmp" alt="" /> is The external natural derivative, and <img src="Edit_3b36ed6b-e780-46de-925e-e3cf7c6a125f.bmp" alt="" />: [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of <em>f </em>with a) <em>f<sub>i </sub></em>> 0, b) <em>f<sub>i </sub></em>< 0, and c) <em>f<sub>i </sub></em>= 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings. </p>
文摘In this article, we establish the existence of positive solution for the following Hadamard fractional singular boundary value problem where is continuous and singular at t = a, t = b and x = 0. Further, is Hadamard fractional derivative of order μ. Moreover, the existence of positive solution has been established using fixed point index for a completely continuous map in a cone. Also, an example is included to show the validity of our result.
基金Supported by the National Natural Science Foundation of China (No.10871116)Natural Science Foundation of Shandong Province (No.ZR2009AM006)
文摘Using the fixed point index in cones, we study the existence of one and two positive solutions to singular second order Neumann boundary value problems under some conditions, which concerns the first eigenvalue of the relevant linear problem. Our results improve and extend some known ones in the previous literature.
基金The paper is supported by Youth Funds of JXUFE,JXJG07436.
文摘In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.
基金Supported by NNSF of China (No.60665001) Educational Department of Jiangxi Province(No.GJJ08358+1 种基金 No.GJJ08359 No.JXJG07436)
文摘In this paper, we study a class of fourth-order Neumann boundary value problem (NBVP for short). By virtue of fixed point index and the spectral theory of linear operators, the existence of positive solutions is obtained under the assumption that the nonlinearity satisfies sublinear or superlinear conditions, which are relevant to the first eigenvalue of the corresponding linear operator.
基金Supported by NNSF of China (No.60665001)Educational Department of Jiangxi Province(No.GJJ08358, No.GJJ08359, No.JXJG07436)
文摘In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.
基金Supported by the National Natural Science Foundation of China(Grant No.11601011)
文摘In this paper, we study two kinds of first-order singular discrete systems.By the fixed point index theory, we investigate the existence and multiplicity of positive periodic solutions of the systems.
基金Supported by National Natural Science Foundation of China (No.10626029, No.10701040)Edu-cational Department of Jiangxi Province (No.GJJ08358, No.GJJ08359, No.JXJG07436)Jiangxi University of Finance and Economics (No.04232015, No.JXCDJG0813).
文摘By virtue of the fixed point indices, we discuss the existence of the multiple positive periodic solutions to singular differential equation with state-dependent delay under the conditions concerning the first eigenvalue of the relevant linear operator. The results in this paper are optimal and totally generalize many present results.
基金supported by the National Natural Science Foundation of China (10971179)the Natural Science Foundation of Liaocheng University (31805)
文摘This paper investigates the existence and multiplicity of nonnegative solutions to a singular nonlinear boundary value problem of second order differential equations with integral boundary conditions in a Banach space. The arguments are based on the construction of a nonempty bounded open convex set and fixed point index theory. Our nonlinearity possesses singularity and first derivative which makes it different with that in [10].
基金Supported by National Natural Science Foundation of China (10626029 10701040+4 种基金 60964005 11161022)Natural Science Foundation of Jiangxi Province (2009GQS0007)Educational Department of Jiangxi Province (JJ0946 GJJ11420)
文摘The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.
基金supported by the National Natural Science Foundation of China (No.10626029No.10701040)+2 种基金Natural Science Foundation of Jiangxi Province (No.2009GQS0007)Educational Department of Jiangxi Province (No.JJ0946)Jiangxi University of Finance and Economics(No.JXCDJG0813)
文摘By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem, where the nonlinear term is allowed to be nonnegative and unbounded.
基金supported by the National Natural Science Foundation of China (10671167)
文摘In this paper, we use cone theory and a new method of computation of fixed point index to study a system of nonlinear Hammerstein type integral equations, and the existence of multiple positive solutions to the system is discussed.
基金supported by Natural Science Foundation of Anhui University of Architecture(20071201)
文摘This paper investigates the existence of positive solutions to systems of second order nonlocal boundary value problems with first order derivatives, in which the nonlinear term is not required to be continuous and involves first order derivatives. The main tool used in this paper is a fixed point index theory in a cone.
文摘This paper deals with the existence of positive solutions to the singular secondorder periodic boundary value problem. We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.
