Electron. J. Differential Equations, Vol. 2016 (2016), No. 232, pp. 1-18.

Combined effects of changing-sign potential and critical nonlinearities in Kirchhoff type problems

Gao-Sheng Liu, Liu-Tao Guo, Chun-Yu Lei

Abstract:
In this article, we study the existence and multiplicity of positive solutions for a class of Kirchhoff type problems involving changing-sign potential and critical growth terms. Using the concentration compactness principle and Nehari manifold, we obtain the existence and multiplicity of nonzero non-negative solutions.

Submitted June 8, 2016. Published August 24, 2016.
Math Subject Classifications: 35D05, 35J60, 58J32.
Key Words: Kirchhoff type equation; critical exponents; changing-sign potential; Nehari manifold.

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Gao-Sheng Liu
Shanghai University of Finance and Economics
Shanghai 200433, China
email: 772936104@qq.com
Liu-Tao Guo
Guizhou Minzu University
Guiyang 550025, China
email: 350630542@qq.com
Chun-Yu Lei
School of Science
Guizhou Minzu University
Guiyang 550025, China
email: leichygzu@sina.cn

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