A three critical point theorem for non-smooth functionals with application in differential inclusions

Proceedings Mathematical Sciences

Shirin Mir²  Ghasem A Afrouzi¹  Mohammad B Ghaemi³ 

[1] Department of Mathematics, Faculty of Mathematics Sciences, University of Mazandaran, Babolsar, Iran$$;Department of Mathematics, Payame Noor University, Tehran, P. O. Box -, Iran$$;Department of Mathematics, Iran University of Science and Technology, Tehran, P. O. Box -, Iran$$

关键词: Locally Lipschitz functions;    differential inclusions;    anti-periodic solution;    critical point.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

A variety of three-critical-point theorems have been established for nonsmooth functionals, based on a minimax inequality. In this paper, a generalized form of a recent result due to Ricceri is introduced for non-smooth functionals and by a few hypotheses, without any minimax inequality, the existence of at least three critical points with a uniform bound on the norms of solutions, is obtained. Also, as an application, our main theorem is used to obtain at least three anti-periodic solutions for a second order differential inclusion.

【 授权许可】

Unknown