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Open Access Research

Existence of periodic solutions for a class of p-Laplacian equations

Xiaojun Chang12* and Yu Qiao3

Author affiliations

1 School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, P.R. China

2 College of Mathematics, Jilin University, Changchun, Jilin, 130012, P.R. China

3 College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, P.R. China

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Citation and License

Boundary Value Problems 2013, 2013:96  doi:10.1186/1687-2770-2013-96

Published: 19 April 2013

Abstract

This paper is devoted to the existence of periodic solutions for the one-dimensional p-Laplacian equation

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where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M2">View MathML</a> (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M3">View MathML</a>), <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M4">View MathML</a>. By using some asymptotic interaction of the ratios <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M5">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M6">View MathML</a> with the Fučík spectrum of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/96/mathml/M7">View MathML</a> related to periodic boundary condition, we establish a new existence theorem of periodic solutions for the one-dimensional p-Laplacian equation.

Keywords:
periodic solutions; p-Laplacian; Fučík spectrum; Leray-Schauder degree; Borsuk theorem