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Annali di Matematica Pura ed Applicata

, Volume 105, Issue 1, pp 221–239 | Cite as

Invariant sets for perturbed semigroups of linear operators

  • Robert H. MartinJr.
Article

Summary

Let E be a Banach space and consider the initial value problem (*) u’(t)=Au(t)+ +B(t,u(t)), t≥0, u(0)=z; where A is the generator of a linear contraction semigroup and B: [0, ∞)×E→E is continuous. The main results of this paper deal with criteria insuring that a closed subset Ω of E is invariant for (*)—that is, z∈Ω implies that a solution u to (*) satisfies u(t)∈Ω for all t≥0.

Keywords

Banach Space Linear Operator Closed Subset Contraction Semigroup Linear Contraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Robert H. MartinJr.
    • 1
  1. 1.RaleighUSA

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