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Open Access Research

Existence of three solutions for a nonlocal elliptic system of ( p , q ) -Kirchhoff type

Guang-Sheng Chen1, Hui-Yu Tang1*, De-Quan Zhang2, Yun-Xiu Jiao3 and Hao-Xiang Wang4

Author Affiliations

1 Department of Construction and Information Engineering, Guangxi Modern Vocational Technology College, Hechi, Guangxi, 547000, China

2 Faculty of Science, Guilin University of Aerospace Industry, Guilin, Guangxi, 541004, China

3 Department of Common Courses, Xinxiang Polytechnic College, Xinxiang, Henan, 453006, China

4 School of Electronic Engineering, Xidian University, Xi’an, Shanxi, 710126, China

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Boundary Value Problems 2013, 2013:175  doi:10.1186/1687-2770-2013-175

Published: 25 July 2013

Abstract

In this paper, we study the solutions of a nonlocal elliptic system of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/175/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/175/mathml/M1">View MathML</a>-Kirchhoff type on a bounded domain based on the three critical points theorem introduced by Ricceri. Firstly, we establish the existence of three weak solutions under appropriate hypotheses; then, we prove the existence of at least three weak solutions for the nonlocal elliptic system of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/175/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/175/mathml/M1">View MathML</a>-Kirchhoff type.

Keywords:
<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/175/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/175/mathml/M1">View MathML</a>-Kirchhoff type system; multiple solutions; three critical points theory