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Nonlinear boundary value problems for second order differential inclusions

Sophia Th. Kyritsi;  Nikolaos M. Matzakos;  Nikolaos S. Papageorgiou — 2005

Czechoslovak Mathematical Journal

In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form x ↦ a ( x , x ' ) ' . In this problem the maximal monotone term is required to be defined everywhere in the state space ℝ N . The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form x ↦ ( a ( x ) x ' ) ' . In this case the maximal...

Nonlinear elliptic differential equations with multivalued nonlinearities

Antonella Fiacca;  Nikolaos M. Matzakos;  Nikolaos S. Papageorgiou;  Raffaella Servadei — 2003

Czechoslovak Mathematical Journal

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 by the upper...

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