Existence and monotone iteration of symmetric positive solutions for integral boundary-value problems with ϕ-Laplacian operator

Tugba S Cerdik,Nuket A Hamal

doi:10.1186/1029-242x-2014-463

Tugba S Cerdik, Nuket A Hamal

Open Access

https://doi.org/10.1186/1029-242x-2014-463

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Abstract

The purpose of this paper is to investigate the existence and iteration of symmetric positive solutions for integral boundary-value problems. An existence result of positive, concave and symmetric solutions and its monotone iterative scheme are established by using the monotone iterative technique. An example is worked out to demonstrate the main result.MSC:34B10, 34B18, 39A10.

Highlights

1 Introduction The existence and multiplicity of positive solutions for linear and nonlinear multi-point boundary-value problems have been widely studied by many authors using a fixed point theorem in cones
Increasing attention is paid to boundary-value problems with integral boundary conditions
In [ – ], the authors used the monotone iterative method to get a positive solution of multi-point boundary-value problems for differential equations

Summary

Introduction

The existence and multiplicity of positive solutions for linear and nonlinear multi-point boundary-value problems have been widely studied by many authors using a fixed point theorem in cones. An increasing interest has been observed in investigating the existence of positive solutions of boundary-value problems for differential equations by using the monotone iterative method. In [ – ], the authors used the monotone iterative method to get a positive solution of multi-point boundary-value problems for differential equations. Motivated by all the works above, in this study, we consider the following secondorder multi-point integral boundary-value problem (BVP):. We investigate here the iteration and existence of symmetric positive solutions for the multi-point integral boundary-value problems with φ-Laplacian To the best of our knowledge, no contribution exists concerning the existence of symmetric positive solutions for multipoint boundary-value problems with integral boundary conditions by applying monotone iterative techniques. For symmetry of h(t), it is easy to show that

If t

Choosing a