Invariant sets for perturbed semigroups of linear operators
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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.
KeywordsBanach Space Linear Operator Closed Subset Contraction Semigroup Linear Contraction
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