Electron. J. Diff. Equ., Vol. 2015 (2015), No. 232, pp. 1-16.

Non-smooth extension of a three critical points theorem by Ricceri with an application to p(x)-Laplacian differential inclusions

Ziqing Yuan, Lihong Huang

Abstract:
We extend a smooth Ricceri three critical-points theorem to a non-smooth case. Our approach is based on the non-smooth analysis. As an application, we obtain the existence of at least three critical points for a p(x)-Laplacian differential inclusion.

Submitted May 20, 2015. Published September 10, 2015.
Math Subject Classifications: 49J20, 35J85, 47J30.
Key Words: Nonsmooth critical point theory; locally Lipschitz; differential inclusion; p(x)-Laplacian.

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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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