Nonconvex and nonmonotone perturbations of evolution inclusions of subdifferential type
type: Item
instance of: scholarly article
title: Nonconvex and nonmonotone perturbations of evolution inclusions of subdifferential type
zbMATH Open document ID: 0727.34055
DOI: 10.1007/BF01946854
author: Nikolaos S. Papageorgiou
published in: Periodica Mathematica Hungarica
publication date: 1990-01-01T00:00:00Z
review text: The note contains an existence theorem for strong solutions of differential inclusions \(\dot x(t)\in -\partial \phi (x(t))-F(t,x(t)),\) in a separable Hilbert space. Here \(\partial \phi\) is the subdifferential of a proper lower semicontinuous convex function \(\phi\) with precompact level sets, and F is a measurable lower semicontinuous multifunction. If \(| F(t,x)|\) is dominated by \(\alpha| \partial \phi (x)|\) with \(\alpha <1\), then a local solution is constructed by means of a fixed point argument. The solution exists globally if an additional one- sided growth assumption holds.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 4200664
zbMATH Keywords: nonlinear evolution equation
zbMATH Keywords: multifunctions
zbMATH Keywords: differential inclusions
reviewed by: Hans Engler
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4200664