A class of quasilinear elliptic hemivariational inequality  problems on unbounded domains

Lijing Xi; Yuying Zhou; Yisheng Huang

doi:10.3934/jimo.2014.10.827

Article Contents

2014, Volume 10, Issue 3: 827-837. Doi: 10.3934/jimo.2014.10.827

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A class of quasilinear elliptic hemivariational inequality problems on unbounded domains

1.
Department of Mathematics, Soochow University, Suzhou 215006
2.
Department of Mathematics, Soochow University, Suzhou, 215006

Received: April 30, 2013

Revised: May 31, 2013

Published: June 2014

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Abstract

In this paper, we are concerned with the existence of solutions of a class of quasilinear elliptic hemivariational inequalities on unbounded domains. This kind of problems is more delicate due to the lack of compact embedding of the Sobolev spaces. By using the Clarke generalized directional derivatives for locally Lipschitz functions and some nonlinear function analysis techniques, such as the Ky Fan theorem for multivalued mappings, the theorem of finite intersection property, etc, we obtain the existence of solutions of the quasilinear elliptic hemivariational inequalities. Unlike those methods used in the references mentioned in this paper, we treat the case of unbounded domain by using the approximation of bounded domains.

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Mathematics Subject Classification: Primary: 47J20; Secondary: 35J20, 49J53.

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