Nonlinear hemivariational inequalities of second order using the method of upper-lower solutions

Kourogenis, Nikolaos; Papageorgiou, Nikolaos

doi:10.1090/S0002-9939-03-06993-4

Nonlinear hemivariational inequalities of second order using the method of upper-lower solutions
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by Nikolaos C. Kourogenis and Nikolaos S. Papageorgiou

Proc. Amer. Math. Soc. 131 (2003), 2359-2369

DOI: https://doi.org/10.1090/S0002-9939-03-06993-4

Published electronically: March 11, 2003

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Abstract:

In this paper we examine a nonlinear hemivariational inequality of second order. The differential operator is set-valued, nonlinear and depends on both $x$ and its gradient $Dx$. The same is true for the zero order term $f$, while the right-hand side nonlinearity satisfies a one-sided Lipschitz condition. We use the method of upper and lower solutions, coupled with truncation and penalization techniques and the fixed point theory for multifunctions in an ordered Banach space.

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