Existence of positive solutions to multi-point third order problems with sign changing nonlinearities (original) (raw)

Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

Acta et Commentationes Universitatis Tartuensis de Mathematica

In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results.

This paper is devoted to the study of the existence and uniqueness of the positive solution for a type of the nonlinear third-order three-point boundary value problem. Our results are based on an iterative method and the Leray-Schauder fixed point theorem.

This work concerned withthe following third-order three point boundaryvalue problem (BVP). Our main objective is to investigatethe existence, uniqueness and existence of positive solutions forthe boundary value problem (P1), by using Banach contractionprinciple, Leray Schauder nonlinear alternative, properties of theGreen function and Guo-Krasnosel'skii fixed point theorem in cone,in the case where the nonlinearity fff is either superlinear orsublinear.