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ON THE METHOD OF APPROXIMATION FOR EVOLUTIONARY INCLUSIONS OF PSEUDOMONOTONE TYPE

Part of: Calculus on manifolds; nonlinear operators Parabolic equations and systems General theory in ordinary differential equations

Published online by Cambridge University Press:  01 February 2008

PAVLO KASYANOV ,
VALERY MELNIK  and
JOSÉ VALERO
PAVLO KASYANOV
Affiliation:
Kyiv Taras Shevchenko University, 01033 Kiev, Ukraine (email: kasyanov@univ.kiev.ua)
VALERY MELNIK
Affiliation:
Institute of Applied and System Analysis, Kiev, Ukraine (email: moreva@mmsa.ntu-kpi.kiev.ua)
JOSÉ VALERO
Affiliation:
Centro de Investigación Operativa, Universidad Miguel Hernández Avda Universidad s/n, 03202 Elche, Alicante, Spain (email: jvalero@umh.es)
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Abstract

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For a large class of operator inclusions, including those generated by maps of pseudomonotone type, we obtain a general theorem on existence of solutions. We apply this result to some particular examples. This theorem is proved using the method of difference approximations.

Keywords

differential inclusionsvariational inequalitiespseudomonotone maps

MSC classification

Secondary: 35K55: Nonlinear parabolic equations 58C06: Set valued and function-space valued mappings 34A40: Differential inequalities 34A60: Differential inclusions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 1 , February 2008 , pp. 115 - 143
Copyright
Copyright © Australian Mathematical Society 2008

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