Stable perturbations of linear differential equations generating a uniformly bounded group

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Abstract

Stability problems for solutions of the differential equation u′(t) = Au+ϵB(t, u) in a Banach space are considered. It is assumed that for ϵ = 0 this equation generates a uniformly bounded group of class C0. Sufficient conditions on B and A are found under which the solutions of this equation are bounded for small ϵ. A linearization principle is proved for this equation under certain conditions on the operator B.

Original languageEnglish
Pages (from-to)1246-1259
Number of pages14
JournalSbornik Mathematics
Volume208
Issue number8
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • Differential equations in a Banach space
  • Stability of solutions
  • stability of solutions
  • differential equations in a Banach space

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