Nonlocal boundary value problems for second-order functional differential equations

We study the existence of a solution to a nonlocal boundary value problem for a class of second-order functional differential equations with piecewise constant arguments. The equation studied includes terms depending on the derivative as well as delay arguments in the derivative.     

Decaying solutions for discrete boundary value problems on the half line

Some nonlocal boundary value problems, associated to a class of functional difference equations on unbounded domains, are considered by means of a new approach. Their solvability is obtained by using properties of the recessive solution to suitable half-linear difference equations, a half-linearization technique and a fixed point theorem in Frechét spaces. The result is applied to derive the existence of nonoscillatory solutions with initial and final data. Examples and open problems complete the paper.     

On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals

We study the existence of positive solutions for the following boundary value problem on infinite interval for second-order functional differential equations:

     

Multiple positive solutions for a functional second-order boundary value problem

By using the Krasnoselskii fixed point theorem on cones in Banach spaces some existence results of positive solutions of a boundary value problem concerning a second-order functional differential equation are given.     

Positive solutions for multi-point boundary value problem on the half-line

This paper presents a variety of existence results for nonlinear multi-point boundary value problem on the half-line. In particular, we consider

     

Multiple positive solutions of boundary value problems for systems of nonlinear second-order differential equations

This paper is concerned with boundary value problems for systems of nonlinear second-order differential equations. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.     

Multiple positive solutions for second-order m-point boundary value problems

In this paper, the second-order m-point boundary value problem

     

Multiple positive solutions of singular second-order m-point boundary value problems

The existence of multiple positive solutions about the singular second-order m-point boundary value problem

     

Multiple positive solutions for discrete nonlocal boundary value problems

In this paper, we investigate a second-order nonlinear difference equation with sign-changing nonlinearity subject to two different sets of nonlocal boundary conditions. The explicit expressions of the associated Green's functions are presented. By using a recently developed fixed point theorem, we establish sufficient conditions for the existence of multiple positive solutions of the 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。     

Positive solutions for nonlinear discrete second-order boundary value problems with parameter dependence

In this paper, we consider the nonlinear discrete boundary value problem

     

Nontrivial solutions of boundary value problems of second-order difference equations

We employ the critical point theory to establish the existence of nontrivial solutions for some boundary value problems of second-order difference equations.     

Eigenvalue criteria for existence of multiple positive solutions to boundary value problems of second-order delay differential equations

Criteria are established for existence of multiple positive solutions to the boundary value problems expressed by second-order delay differential equations of the form

     

Existence theorems for second-order discrete boundary value problems

This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type , where δ>0 is the ratio of odd positive integers, {p_n} and {q_n} are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions.     

Positive solutions for some second-order four-point boundary value problems

In this paper, the second-order four-point boundary value problem

     

Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations

In this paper, the authors consider the boundary value problem

and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)-(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373-2379) are discussed.

     

Weak solutions for anisotropic discrete boundary value problems

In this paper, we prove the existence and uniqueness of weak solutions for a family of discrete boundary value problems for data f which belong to a discrete Hilbert space H. Moreover, as an extension, we prove some existence results of weak solutions for more general data f depending on the solution.