Linearized stability for nonlinear Volterra equations

Stig-Olof Londen, Wolfgang M. Ruess

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)


In the context of the nonlinear Volterra equation u(t)+∫0tb(t-s)Au(s)ds∋u0,t≥ 0 , with A⊂ X× X an m- α-accretive operator in a Banach space X, and b a completely positive kernel, we establish a principle of linearized stability of an equilibrium solution ue under the assumption of the existence of a resolvent-differential A~ ⊂ X× X of A at ue with the property that (A~ - ωI) is accretive for some ω> 0.

Original languageEnglish
Pages (from-to)473-483
Number of pages11
JournalJournal of Evolution Equations
Issue number1
Publication statusPublished - 1 Mar 2017
MoE publication typeA1 Journal article-refereed


  • Accretive operators
  • Linearized stability
  • Nonlinear Volterra equations


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