Invariant sets for a class of perturbed differential equations of retarded type |
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Authors: | N. Pavel F. Iacob |
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Affiliation: | (1) Seminarul Matematic, Universitatea Iaşi, Romania |
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Abstract: | LetX be a Banach space and leta, b, q be real numbers such thata,q>0. Denote byD a locally closed subset ofX. A necessary and sufficient condition for the existence of a mild solutionu∈C([a−q, b 1],X),a 1<b, to the differential equationdu(t)/dt=Au(t)+f(t, u t), such thatu:[a,b 1]→D, u a=ϕ is given. The linear operatorA is the generator of aC 0 semigroupT(t), t≧0, withT(t) compact fort>0,f: [a, b)×C([−q,0],D λ)→X is continuous and ϕ∈C([−q,0],D λ) with ϕ(0)∈D. D λ is a neighbourhood ofD. Applications to parabolic partial differential equations with retarded argument are given. |
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