Open Access Research

Triple solutions of complementary Lidstone boundary value problems via fixed point theorems

Patricia JY Wong

Author Affiliations

School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

Boundary Value Problems 2014, 2014:125  doi:10.1186/1687-2770-2014-125

Published: 20 May 2014

Abstract

We consider the following complementary Lidstone boundary value problem:

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By using fixed point theorems of Leggett-Williams and Avery, we offer several criteria for the existence of three positive solutions of the boundary value problem. Examples are also included to illustrate the results obtained. We note that the nonlinear term F depends on <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/125/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/125/mathml/M2">View MathML</a> and this derivative dependence is seldom investigated in the literature and a new technique is required to tackle the problem.

MSC: 34B15, 34B18.

Keywords:
positive solutions; complementary Lidstone boundary value problems; derivative-dependent nonlinearity; fixed point theorems