ON THE POSITIVE SOLUTIONS FOR THIRD ORDER BOUNDARY VALUE PROBLEM

Moustafa El-Shahed (Kingdom of Saudi Arabia)

Received February 6, 2007

Abstract

In this paper, we investigate the problem of existence of positive solutions for the nonlinear third order boundary value problem: where l is a positive parameter. By using Krasnoselskii’s fixed point theorem of cone, we establish various results on the existence of positive solutions of the boundary value problem. Under various assumptions on and we give the intervals of the parameter l which yield the existence of the positive solutions. An example is also given to illustrate the main results.

Keywords and phrases: third order, boundary-value problem, Krasnoselskii’s fixed-point theorem, Green’s function, positive solution.