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

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.

Keywords

• Sobolev space
• periodic solution
• locally Lipschitz potential
• AR-condition
• nonsmooth C-condition
• the least action principle
• mountain pass lemma