SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Existence of homoclinic orbits for a class of p-Laplacian systems in a weighted Sobolev space

Xiubo Shi1, Qiongfen Zhang1* and Qi-Ming Zhang2

Author affiliations

1 College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, P.R. China

2 College of Science, Hunan University of Technology, Zhuzhou, Hunan, 412000, P.R. China

For all author emails, please log on.

Citation and License

Boundary Value Problems 2013, 2013:137  doi:10.1186/1687-2770-2013-137

Published: 24 May 2013

Abstract

By applying the mountain pass theorem and symmetric mountain pass theorem in critical point theory, the existence of at least one or infinitely many homoclinic solutions is obtained for the following p-Laplacian system:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M2">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M3">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M4">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M5">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M6">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M7">View MathML</a> are not periodic in t.

MSC: 34C37, 35A15, 37J45, 47J30.

Keywords:
homoclinic solutions; variational methods; weighted <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/137/mathml/M8">View MathML</a> space; p-Laplacian systems