ArticleOriginal scientific text
Title
Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions
Authors 1, 2
Affiliations
- Center for Mathematical Sciences, Munich University of Technology (TUM), Arcisstr. 21, D-80333 München, Germany
- Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Abstract
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.
Keywords
Dirichlet, maximal monotone operator, Yosida approximation, monotone operator, resolvent operator, measurable selection, demicontinuous operator, Neumann and periodic problems, coercive operator, projection theorem
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Pages:
69-92
Main language of publication
English
Received
1999-07-20
Published
2000
Exact and natural sciences