Electron. J. Diff. Equ., Vol. 2014 (2014), No. 136, pp. 1-14.

Periodic solutions for second-order differential inclusions with nonsmooth potentials under weak AR-conditions

Lizhen Chen, Qinghua Zhang, Gang Li

In this article, we study a periodic second-order differential inclusions with locally Lipschitz potentials. By means of the least action principle and the minimax principle of nonsmooth type, we prove the existence of two nontrivial periodic solutions under the weak AR-conditions. The method developed in this paper can be applied for studying second-order differential inclusions of periodic type, and for elliptic equations with Neumann boundary condition.

Submitted April 3, 2014. Published June 11, 2014.
Math Subject Classifications: 34K37, 46E35, 47H10.
Key Words: Sobolev space; periodic solution; locally Lipschitz potential; AR-condition; nonsmooth C-condition; the least action principle; mountain pass lemma.

Show me the PDF file (252 KB), TEX file, and other files for this article.

Lizhen Chen
Department of Applied Mathematics
Shanxi University of Finance and Economics
Taiyuan, Shanxi, 030006, China
email: chenlz409@126.com
Qinghua Zhang
Department of Mathematics, Nantong University
Nantong, Jiangsu 226007, China
email: zhangqh1971@126.com
  Gang Li
Department of Mathematics, Yangzhou University
Yangzhou, Jiangsu 225002, China
email: yzgangli@163.com

Return to the EJDE web page