Existence and multiplicity for positive solutions of a second-order multi-point discrete boundary value problem

We investigate the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations with multi-point boundary conditions.     

On existence and multiplicity of positive solutions to singular multi-point boundary value problems

The existence and multiplicity of positive solutions are established for the multi-point boundary value problem

     

Twin positive solutions for quasi-linear multi-point boundary value problems

In this paper, we investigate two classes of quasi-linear multi-point boundary value problems with sign-changing nonlinearity. By applications of fixed point index theory, sufficient conditions for the existence of twin positive solutions are established.     

Existence and multiplicity of symmetric positive solutions for three-point boundary value problem

In this paper, we are concerned with the existence and multiplicity of symmetric positive solutions for the following second-order three-point boundary value problem

     

Positive solutions for a system of second-order multi-point boundary value problems

In this paper, we present some results for positive solutions of a system of nonlinear second-order ordinary differential equations subject to multi-point boundary conditions.     

Existence and multiplicity of solutions for fourth-order boundary value problems with parameters

In this paper we study the existence and multiplicity of the solutions for the fourth-order boundary value problem (BVP) u(4)(t)+ηu^″(t)−ζu(t)=λf(t,u(t)), 0<t<1, u(0)=u(1)=u^″(0)=u^″(1)=0, where is continuous, ζ,η∈R and λ∈R⁺ are parameters. By means of the idea of the decomposition of operators shown by Chen [W.Y. Chen, A decomposition problem for operators, Xuebao of Dongbei Renmin University 1 (1957) 95-98], see also [M. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Gostehizdat, Moscow, 1956], and the critical point theory, we obtain that if the pair (η,ζ) is on the curve ζ=−η²/4 satisfying η<2π², then the above BVP has at least one, two, three, and infinitely many solutions for λ being in different interval, respectively.     

Existence of positive solutions for a system of semipositone coupled discrete boundary value problems

We study the existence of positive solutions for a system of nonlinear second-order difference equations with parameters and sign-changing nonlinearities, subject to multi-point coupled boundary conditions. In the proof of our main theorems we use the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel'skii fixed point theorem.     

Positive solutions for a system of second-order multi-point discrete boundary value problems

We present some results for positive solutions of a system of nonlinear second-order difference equations, subject to multi-point boundary conditions.     

Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations

In this work, we investigate existence and uniqueness of solutions for a class of nonlinear multi-point boundary value problems for fractional differential equations. Our analysis relies on the Schauder fixed point theorem and the Banach contraction principle.     

Existence of positive solutions of Lidstone boundary value problems

We show that there exists at least one positive solution for Lidstone boundary value problem

     

一类二阶离散Neumann边值问题正解的存在性

研究一类二阶离散Neumann边值问题正解的存在性,运用不动点指数理论获得了方程存在正解的最优条件,并给出一个具体例子说明这一结果。     

Multiple positive solutions for multi-point boundary value problems with a p-Laplacian on the half-line

This paper deals with the existence of multiple positive solutions for multi-point boundary value problems with p-Laplacian on infinite intervals. By using three fixed point theorems in cones, especially a five functionals fixed point theorem, we obtain the sufficient conditions for the existence of at least one, two and three positive solutions, respectively. Two examples are also given in this paper to illustrate the main results.     

Nodal solutions of multi-point boundary value problems

We study the nonlinear boundary value problem consisting of the equation y^″+w(t)f(y)=0 on [a,b] and a multi-point boundary condition. By relating it to the eigenvalues of a linear Sturm-Liouville problem with a two-point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. We also discuss the changes in the existence question for different types of nodal solutions as the problem changes.     

Existence of positive solutions for the system of higher order two-point boundary value problems

In this paper, we establish the existence of at least one and two positive solutions for the system of higher order boundary value problems by using the Krasnosel’skii fixed point theorem.     

Existence of positive solutions for three-point boundary value problems at resonance

With the help of the theorem of a fixed point index for A-proper semilinear operators established by Cremins, we get a existence theorem concerning the existence of positive solution for the second order ordinary differential equation of three-point boundary value problems at resonance.