Boundary value problems for systems of second-order functional differential equations.
Staněk, Svatoslav (2000)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Displaying similar documents to “A note on solutions of semilinear equations at resonance in a cone”
Boundary value problems for systems of second-order functional differential equations.
A nonlinear periodic system with nonsmooth potential of indefinite sign
Michael E. Filippakis, Nikolaos S. Papageorgiou (2006)
Archivum Mathematicum
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In this paper we consider a nonlinear periodic system driven by the vector ordinary -Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.
Periodic solutions for differential inclusions in
Michael E. Filippakis, Nikolaos S. Papageorgiou (2006)
Archivum Mathematicum
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We consider first order periodic differential inclusions in . The presence of a subdifferential term incorporates in our framework differential variational inequalities in . We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.
Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions
Ralf Bader, Nikolaos Papageorgiou (2000)
Annales Polonici Mathematici
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We consider a quasilinear vector differential equation which involves the p-Laplacian and a maximal monotone map. The boundary conditions are nonlinear and are determined by a generally multivalued, maximal monotone map. We prove two existence theorems. The first assumes that the maximal monotone map involved is everywhere defined and in the second we drop this requirement at the expense of strengthening the growth hypothesis on the vector field. The proofs are based on the theory of...
Extremal solutions and relaxation for second order vector differential inclusions
Evgenios P. Avgerinos, Nikolaos S. Papageorgiou (1998)
Archivum Mathematicum
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In this paper we consider periodic and Dirichlet problems for second order vector differential inclusions. First we show the existence of extremal solutions of the periodic problem (i.e. solutions moving through the extreme points of the multifunction). Then for the Dirichlet problem we show that the extremal solutions are dense in the -norm in the set of solutions of the “convex” problem (relaxation theorem).