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elliptic hemivariational inequality

Proceedings of the Edinburgh Mathematical Society (1)

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ON EIGENVALUE PROBLEMS FOR ELLIPTIC HEMIVARIATIONAL INEQUALITIES
Zhenhai Liu, Guifang Liu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 51 / Issue 2 / June 2008

Published online by Cambridge University Press:

28 July 2008, pp. 407-419
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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.