Existence theorems for elliptic hemivariational inequalities involving the -Laplacian.

Kourogenis, Nikolaos C.; Papageorgiou, Nikolaos S.

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Solutions for nonlinear variational inequalities with a nonsmooth potential.

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Nonlinear elliptic differential equations with multivalued nonlinearities

Antonella Fiacca, Nikolaos M. Matzakos, Nikolaos S. Papageorgiou, Raffaella Servadei (2003)

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In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all $ℝ$ . Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed...