Displaying similar documents to “The Neumann problem for quasilinear differential equations”

Nonlinear boundary value problems for second order differential inclusions

Sophia Th. Kyritsi, Nikolaos M. Matzakos, Nikolaos S. Papageorgiou (2005)

Czechoslovak Mathematical Journal

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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...

Nonlinear elliptic differential equations with multivalued nonlinearities

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

Czechoslovak Mathematical Journal

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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...

Periodic solutions for nonlinear evolution inclusions

Dimitrios A. Kandilakis, Nikolaos S. Papageorgiou (1996)

Archivum Mathematicum

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In this paper we prove the existence of periodic solutions for a class of nonlinear evolution inclusions defined in an evolution triple of spaces ( X , H , X * ) and driven by a demicontinuous pseudomonotone coercive operator and an upper semicontinuous multivalued perturbation defined on T × X with values in H . Our proof is based on a known result about the surjectivity of the sum of two operators of monotone type and on the fact that the property of pseudomonotonicity is lifted to the Nemitsky operator,...