Lizhen Chen, Qinghua Zhang, Gang Li
Abstract:
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.
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Lizhen Chen Department of Applied Mathematics Shanxi University of Finance and Economics Taiyuan, Shanxi, 030006, China email: chenlz409@126.com |
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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 |
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