Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions

• Autorzy: Ralf Bader , Nikolaos S. Papageorgiou
• Języki publikacji: EN

Abstrakty

EN

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 operators of monotone type and on the Leray-Schauder fixed point theorem. At the end we present some special cases (including the classical Dirichlet, Neumann and periodic problems), which illustrate the general and unifying features of our work.

Słowa kluczowe

EN

Dirichlet   maximal monotone operator   Yosida approximation   monotone operator   resolvent operator   measurable selection   demicontinuous operator   Neumann and periodic problems   coercive operator   projection theorem  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 73
• Numer: 1
• Strony: 69-92

Daty

wydano

2000

otrzymano

1999-07-20

Twórcy

autor

Ralf Bader

• Center for Mathematical Sciences, Munich University of Technology (TUM), Arcisstr. 21, D-80333 München, Germany

autor

Nikolaos S. Papageorgiou

• Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

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