Geodesic
Periodic solutions for second-order differential inclusions with nonsmooth potentials under weak AR-conditions
Electronic journal of differential equations, Tome 2014 (2014)
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.
Classification : 34K37, 46E35, 47H10
Keywords: Sobolev space, periodic solution, locally Lipschitz potential, AR-condition, nonsmooth C-condition, the least action principle, mountain pass lemma 
@article{EJDE_2014__2014__a22,
     author = {Chen,  Lizhen and Zhang,  Qinghua and Li,  Gang},
     title = {Periodic solutions for second-order differential inclusions with nonsmooth potentials under weak {AR-conditions}},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1305.34029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a22/}
}
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%A Zhang,  Qinghua
%A Li,  Gang
%T Periodic solutions for second-order differential inclusions with nonsmooth potentials under weak AR-conditions
%J Electronic journal of differential equations
%D 2014
%V 2014
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%G en
%F EJDE_2014__2014__a22
Chen,  Lizhen; Zhang,  Qinghua; Li,  Gang. Periodic solutions for second-order differential inclusions with nonsmooth potentials under weak AR-conditions. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a22/