Second-order Multi-point Boundary Value Problem Research Articles

On a system of second-order multi-point boundary value problems on time scales

This paper is concerned with the existence and nonexistence of positive solutions for a system of nonlinear second order dynamic equations with multi-point boundary conditions on time scales.

Existence of Nontrivial Solutions for Some Second-Order Multipoint Boundary Value Problems

By using fixed point theorems with lattice structure, the existence of negative solution and sign-changing solution for some second-order multipoint boundary value problems is obtained.

On a Singular Second-Order Multipoint Boundary Value Problem at Resonance

The aim of this paper is to derive existence results for a second-order singular multipoint boundary value problem at resonance using coincidence degree arguments.

Global Structure of Positive Solutions for Some Second-Order Multipoint Boundary Value Problems

We investigate in this paper the following second-order multipoint boundary value problem:-(Lφ)(t)=λf(t,φ(t)),0≤t≤1,φ′0=0,φ1=∑i=1m-2βiφηi. Under some conditions, we obtain global structure of positive solution set of this boundary value problem and the behavior of positive solutions with respect to parameterλby using global bifurcation method. We also obtain the infinite interval of parameterλabout the existence of positive solution.

Existence of three solutions for impulsive multi-point boundary value problems

This paper is devoted to the study of the existence of at least three classical solutions for a second-order multi-point boundary value problem with impulsive effects. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results. Also by presenting an example, we ensure the applicability of our results.

Existence of three symmetric positive solutions for a second-order multi-point boundary value problem on time scales

AbstractIn this article, we investigate the existence of at least three symmetric positive solutions of a second-order multi-point boundary value problem on time scales. The ideas involve Bai and Ge’s fixed point theorem. As an application, we give an example to demonstrate our main result.MSC:34B10, 34B18, 39A10.

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

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

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.

New Wavelets Collocation Method for Solving Second-Order Multipoint Boundary Value Problems Using Chebyshev Polynomials of Third and Fourth Kinds

This paper is concerned with introducing two wavelets collocation algorithms for solving linear and nonlinear multipoint boundary value problems. The principal idea for obtaining spectral numerical solutions for such equations is employing third- and fourth-kind Chebyshev wavelets along with the spectral collocation method to transform the differential equation with its boundary conditions to a system of linear or nonlinear algebraic equations in the unknown expansion coefficients which can be efficiently solved. Convergence analysis and some specific numerical examples are discussed to demonstrate the validity and applicability of the proposed algorithms. The obtained numerical results are comparing favorably with the analytical known solutions.

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.

On a system of second-order multi-point boundary value problems

We study the existence of positive solutions for a system of nonlinear second-order ordinary differential equations subject to some multi-point boundary conditions. The nonexistence of positive solutions is also investigated.

Reproducing kernel method for singular multi-point boundary value problems

Purpose: In this paper, we shall present an algorithm for solving more general singular second-order multi-point boundary value problems. Methods: The algorithm is based on the quasilinearization technique and the reproducing kernel method for linear multi-point boundary value problems. Results: Three numerical examples are given to demonstrate the efficiency of the present method. Conclusions: Obtained results show that the present method is quite efficient.

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 of positive solutions for semipositone multi-point boundary value problems

In this paper, the existence of positive solutions for a semipositone second-order multi-point boundary value problem is investigated. By using Krasnosel’skii’s fixed point theorem, sufficient conditions that guarantee the existence of at least one positive solution are obtained.

Solutions to a second-order multi-point boundary value problem at resonance

This article deals with the following second-order multi-point boundary value problem x ' ' ( t ) = f ( t , x ( t ) , x ' ( t ) ) + e ( t ) , t ∈ ( 0 , 1 ) , x ' ( 0 ) = ∑ i = 1 m α i x ' ( ξ 1 ) , x ( 1 ) = ∑ j = 1 n β j x ( η j ) . Under the resonance conditions ∑ t = 1 m α i = 1 , ∑ j = 1 n β j = 1 , ∑ j = 1 n β j η j = 1 , by applying the coincidence degree theory, some existence results of the problem are established. The emphasis here is that the dimension of the linear operator is two. In this paper, we extend and improve some previously known results like the ones in the references.

Asymptotic solutions of singularly perturbed second-order differential equations and application to multi-point boundary value problems

In this work, a singularly perturbed second-order ordinary differential equation is solved by applying a new Liouville–Green transform and the asymptotic solutions are obtained. As an application, we employ our results in discussing a second-order multi-point boundary value problem.

Multi-point boundary value problem for optimal bridge design

Based upon He's homotopy perturbation and variational iteration methods, we present a method for approximate solutions of nonlinear second-order multi-point boundary value problems (BVPs) in bridge design. Two numerical experiments are carried out to demonstrate the efficiency of the present method. The results reveal that the proposed method is very effective for second-order multi-point BVPs in bridge design.

Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line

This paper investigates the second-order multipoint boundary value problem on the half-line ,, , , , where , , , , and is continuous. We establish sufficient conditions to guarantee the existence of unbounded solution in a special function space by using nonlinear alternative of Leray-Schauder type. Under the condition that is nonnegative, the existence and uniqueness of unbounded positive solution are obtained based upon the fixed point index theory and Banach contraction mapping principle. Examples are also given to illustrate the main results.

Successive iteration and positive solutions for a second-order multi-point boundary value problem on a half-line

This paper deals with the existence of positive solutions for some second-order multi-point boundary value problem on the half-line. Our approach is based on the fixed point theorem and the monotone iterative technique. Without the assumption of the existence of lower and upper solutions, we obtain not only the existence of positive solutions for the problems, but also establish iterative schemes for approximating the solutions.

Existence of Positive Solutions for Multipoint Boundary Value Problem with p-Laplacian on Time Scales

We consider the existence of positive solutions for a class of second-order multi-point boundary value problem with -Laplacian on time scales. By using the well-known Krasnosel'ski's fixed-point theorem, some new existence criteria for positive solutions of the boundary value problem are presented. As an application, an example is given to illustrate the main results.