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ON EIGENVALUE PROBLEMS FOR ELLIPTIC HEMIVARIATIONAL INEQUALITIES

Published online by Cambridge University Press:  28 July 2008

Zhenhai Liu  and
Guifang Liu
Zhenhai Liu
Affiliation:
Department of Mathematics, Central South University, Changsha, Hunan 410075, China (zhhliu@mail.csu.edu.cn)
Guifang Liu
Affiliation:
Department of Mathematics, Hunan City University, Yiyang, Hunan 413049, China
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Abstract

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This paper is devoted to the Dirichlet problem for quasilinear elliptic hemivariational inequalities at resonance as well as at non-resonance. Using Clarke's notion of the generalized gradient and the property of the first eigenfunction, we also build a Landesman–Lazer theory in the non-smooth framework of quasilinear elliptic hemivariational inequalities.

Keywords

Primary 35B3447J2049J4065N25elliptic hemivariational inequalitygeneralized Clarke subdifferentialpseudo-monotone operatorexistence of solutions
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 2 , June 2008 , pp. 407 - 419
Copyright
Copyright © Edinburgh Mathematical Society 2008