Discrete First-Order Three-Point Boundary Value Problem

Discrete First-Order Three-Point Boundary Value Problem

Abstract We study difference equations which arise as discrete approximations to three-point boundary value problems for systems of first-order ordinary differential equations. We obtain new results of the existence of solutions to the discrete problem by employing Euler’s method. The existence of solutions are proven by the contraction mapping theorem and the Brouwer fixed point theorem in Euc...

Three-Point Boundary Value Problems for Second-Order Discrete Equations

We formulate existence results for solutions to discrete equations which approximate three-point boundary value problems for second-order ordinary differential equations. c © 2003 Elsevier Science Ltd. All rights reserved. Keywords—Three-point boundary value problem, Difference equations, Brouwer degree, Secondorder ordinary differential equations.

First-order three-point boundary value problems at resonance

On a Third-Order Three-Point Boundary Value Problem

where η ∈ 0, 1 , α, β ∈ R, f ∈ C 0, 1 × R,R . The parameters α and β are arbitrary in R such that 1 2α 2βη − 2β / 0. Our aim is to give new conditions on the nonlinearity of f , then using Leray-Schauder nonlinear alternative, we establish the existence of nontrivial solution. We only assume that f t, 0 / 0 and a generalized polynomial growth condition, that is, there exist two nonnegative func...

Positive Solutions for Discrete Third-order Three-point Boundary Value Problem

In this paper, the existence of multiple positive solutions for a class of third-order three-point discrete boundary value problem is studied by applying algebraic topology method. Keywords—Positive solutions, Discrete boundary value problem, Third-order, Three-point, Algebraic topology