Dichotomies for Abstract Semilinear Equations

Y. H. Chang, R. H. Martin

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Abstract

In this paper we present results concerning the existence of solutions in certain abstract semilinear equations and the asymptomatic behavior of these solutions. We also study the sufficient conditions of the conditional stability for the zero solution. The basic techniques used are Lyapunov-like methods and fixed point theory for differential equations in Banach space. However, the improvement here is that it can be applied directly to non-linear equations and hence, we do not need to assume that the differential equation can be linearized.

Original languageEnglish
Pages (from-to)194-214
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume189
Issue number1
DOIs
Publication statusPublished - 1995 Jan 1

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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