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Open Access Research

Existence and uniqueness of solutions for fourth-order periodic boundary value problems under two-parameter nonresonance conditions

He Yang1*, Yue Liang2 and Pengyu Chen1

Author Affiliations

1 Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

2 Science College, Gansu Agricultural University, Lanzhou, 730070, People’s Republic of China

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Boundary Value Problems 2013, 2013:14  doi:10.1186/1687-2770-2013-14

Published: 4 February 2013

Abstract

This paper deals with the existence and uniqueness of solutions of the fourth-order periodic boundary value problem

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/14/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/14/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/14/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/14/mathml/M2">View MathML</a> is continuous. Under two-parameter nonresonance conditions described by rectangle and ellipse, some existence and uniqueness results are obtained by using fixed point theorems. These results improve and extend some existing results.

MSC: 34B15.

Keywords:
existence; uniqueness; two-parameter nonresonance condition; equivalent norm