Existence and asymptotic behavior of a functional differential equation in Banach space |
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Authors: | Samuel M Rankin |
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Affiliation: | Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506 U.S.A. |
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Abstract: | Existence and asymptotic behavior of solutions are given for the equation u′(t) = ?A(t)u(t) + F(t,ut) (t ? 0) and u0 = ? ? C([?r,0]; X) C. The space X is a Banach space; the family of unbounded linear operators defined on D(A) ? X → X generates a linear evolution system and F: C → X is continuous with respect to a fractional power of A(t0) for some t0 ? [0, T]. |
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