Open Access Research

Existence of multiple positive solutions for fourth-order boundary value problems in Banach spaces

Yujun Cui1* and Jingxian Sun2

Author Affiliations

1 Department of Mathematics, Shandong University of Science and Technology, Qingdao, 266590, P.R. China

2 Department of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu, 221116, P.R. China

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Boundary Value Problems 2012, 2012:107 doi:10.1186/1687-2770-2012-107

Published: 9 October 2012

Abstract

This paper deals with the positive solutions of a fourth-order boundary value problem in Banach spaces. By using the fixed-point theorem of strict-set-contractions, some sufficient conditions for the existence of at least one or two positive solutions to a fourth-order boundary value problem in Banach spaces are obtained. An example illustrating the main results is given.

MSC: 34B15.

Keywords:
<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/107/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/107/mathml/M1">View MathML</a>-positive operator; boundary value problem; positive solution; fixed-point theorem; measure of noncompactness