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Doubly nonlinear evolution equations with non‐monotone perturbations
Author(s) -
Akagi Goro
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700647
Subject(s) - monotone polygon , banach space , mathematics , nonlinear system , fixed point theorem , regular polygon , limiting , fixed point , pure mathematics , mathematical analysis , physics , geometry , mechanical engineering , quantum mechanics , engineering
The local (in time) existence of strong solutions to Cauchy problems for doubly nonlinear abstract evolution equations with non‐monotone perturbations in reflexive Banach spaces is proved under appropriate assumptions, which allow the case where solutions of the corresponding unperturbed problem may not be unique. To prove the existence, a couple of approximate problems are introduced and delicate limiting procedures are discussed by using various tools from convex analysis and the Kakutani‐Ky Fan fixed point theorem. Furthermore, an application of the preceding abstract theory to a nonlinear PDE is also given. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)