On a boundary value problem with integral boundary conditions

We study the existence of positive solutions of second-order ordinary differential equations with integral boundary conditions. The result generalizes the conditions obtained in [1] for the existence of positive solutions.     

Multiplicity of sign-changing solutions for some four-point boundary value problem

In this paper we obtain using Leray–Schauder degree theory some multiplicity results for sign-changing solutions of a four-point boundary value problem. We assume the existence of a pair of strict lower and upper solutions and some additional conditions on the nonlinear term f$f$.     

Positive solutions to a new kind Sturm-Liouville-like four-point boundary value problem

In this paper, we considered the following four-point boundary value problem

     

共振情形下四点泛函边值问题解的存在性

运用Mawhin重合度理论,讨论了一类二阶四点泛函边值问题解的存在性和多解性.分别在非线性项f有界和无界的条件下,获得了此类泛函边值问题解的存在性结果.     

On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints

We deal with the problems of four boundary points conditions for both differential inclusions and differential equations with and without moving constraints. Using a very recent result we prove existence of generalized solutions for some differential inclusions and some differential equations with moving constraints. The results obtained improve the recent results obtained by Papageorgiou and Ibrahim-Gomaa. Also by means of a rather different approach based on an existence theorem due to O. N. Ricceri and B. Ricceri we prove existence results improving earlier theorems by Gupta and Marano.     

On a boundary value problem of the theory of oscillations with parameter-dependent boundary conditions

A homogeneous second order differential equation with homogeneous boundary conditions dependent on the parameter, is investigated. Such an equation is obtained in the course of solution of the problem of characteristic oscillations of an ideal incompressible fluid in an elastic vessel, when the method of separation of variables is used. We prove the completeness of the system of eigenfunctions of our boundary value problem and we derive the expansion of an arbitrary, piecewise-continuous function into a series in terms of these eigenfunctions.     

On the Sturm-Liouville-type boundary value problem

The problems of existence, uniqueness and continuous dependence on parameter of solutions of the nonlinear boundary value problem of Sturm-Liouville type for ordinary differential equations are considered. The well-known Banach fixed point theorem is used to establish results.     

On the conjugate boundary value problem

We study the conjugate boundary-value problem with boundary conditions whose orders can be as large as the order of the differential equation or larger. We construct the Green's function of the problem over the entire space when the separating surface is a hyperplane, and we describe its properties. Bibliography: 6 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 20–24.     

Positive solutions for fractional four-point boundary value problems

In this paper, a fractional four-point boundary value problem is considered. By means of fixed-point theorems and successive iteration method, some results on the existence, multiplicity and uniqueness of positive solutions are obtained.     

Upper and lower solution method for a fourth-order four-point boundary value problem on time scales

In this work, we consider a fourth-order four-point boundary value problem on time scales. We establish criteria for the existence of a solution by developing the upper and lower solution method and the monotone iterative technique.     

On efficient numerical methods for an initial-boundary value problem with nonlocal boundary conditions

Many physical phenomena are modeled by nonclassical hyperbolic boundary value problems with nonlocal boundary conditions. In this paper, the problem of solving the one-dimensional wave equation subject to given initial and non-local boundary conditions is considered. These non-local conditions arise mainly when the data on the boundary cannot be measured directly. Several finite difference methods with low order have been proposed in other papers for the numerical solution of this one dimensional non-classic boundary value problem. Here, we derive a new family of efficient three-level algorithms with higher order to solve the wave equation and also use a Simpson formula with higher order to approximate the integral conditions. Additionally, the fourth-order formula is also adapted to nonlinear equations, in particular to the well-known nonlinear Klein–Gordon equations which many physical problems can be modeled with. Numerical results are presented and are compared with some existing methods showing the efficiency of the new algorithms.     

On a two-point boundary value problem of duffing type equation with dirichlet conditions

An existence and uniqueness result concerned with the Diriehlet boundary value prob-lem u“ cu‘ g(t,u)=e(t),u(0)=u(π)=0 is offered.     

On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order

In this paper, we prove the existence and uniqueness of solutions for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q ∈ (1, 2] by applying some standard fixed point theorems. An illustrative example is also presented.