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

Ralf Bader; Nikolaos Papageorgiou

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 1, page 69-92
  • ISSN: 0066-2216

Abstract

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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 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.

How to cite

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Bader, Ralf, and Papageorgiou, Nikolaos. "Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions." Annales Polonici Mathematici 73.1 (2000): 69-92. <http://eudml.org/doc/262597>.

@article{Bader2000,
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.},
author = {Bader, Ralf, Papageorgiou, Nikolaos},
journal = {Annales Polonici Mathematici},
keywords = {Dirichlet; maximal monotone operator; Yosida approximation; monotone operator; resolvent operator; measurable selection; demicontinuous operator; Neumann and periodic problems; coercive operator; projection theorem; quasilinear vector differential equations; nonlinear boundary conditions},
language = {eng},
number = {1},
pages = {69-92},
title = {Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions},
url = {http://eudml.org/doc/262597},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Bader, Ralf
AU - Papageorgiou, Nikolaos
TI - Quasilinear vector differential equations with maximal monotone terms and nonlinear boundary conditions
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 1
SP - 69
EP - 92
AB - 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.
LA - eng
KW - Dirichlet; maximal monotone operator; Yosida approximation; monotone operator; resolvent operator; measurable selection; demicontinuous operator; Neumann and periodic problems; coercive operator; projection theorem; quasilinear vector differential equations; nonlinear boundary conditions
UR - http://eudml.org/doc/262597
ER -

References

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