Electron. J. Diff. Equ., Vol. 2015 (2015), No. 193, pp. 1-18.

Existence of solutions for p(x)-Kirchhoff type problems with non-smooth potentials

Ziqing Yuan, Lihong Huang

Abstract:
We consider a class of p(x)-Kirchhoff type problem with a subdifferential term and a discontinuous perturbation. Assuming the existence of an ordered pair of appropriately defined upper and lower solutions, by the method of lower-upper solutions, penalization techniques, truncations, and results from nonlinear and multivalued analysis, we show the existence of solutions, and of extremal solutions in the interval defined by the lower and upper solution.

Submitted April 16, 2015. Published July 22, 2015.
Math Subject Classifications: 35J20, 34B15, 49J52.
Key Words: Extremal solutions; fixed point; p(x)-Kirchhoff type problem; upper and lower solutions.

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Ziqing Yuan
College of Mathematics and Econometrics
Hunan University
Changsha, Hunan 410082, China
email: junjyuan@sina.com
Lihong Huang
College of Mathematics and Econometrics
Hunan University
Changsha, Hunan 410082, China
email: lhhuang@hnu.edu.cn

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