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.
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| Lizhen Chen |
Department of Applied Mathematics
Shanxi University of Finance and Economics
Taiyuan, Shanxi, 030006, China
| Qinghua Zhang |
Department of Mathematics, Nantong University
Nantong, Jiangsu 226007, China
| Gang Li |
Department of Mathematics, Yangzhou University
Yangzhou, Jiangsu 225002, China
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