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Solvability of Degenerate Semilinear Parabolic Functional Differential Equations

Authors:	Vlasenko L. A.

Affiliation:	(1) Kiev National University, Kiev; Kharkov National University, Kharkov

Abstract:	We obtain local and global theorems on the existence and uniqueness of a solution of the semilinear functional differential equation $frac{d}{{dt}}left[ {Auleft( t right)} right] + Buleft( t right) = fleft( {t,u_t } right)$ in a Banach space with a parabolic pencil of operators A + B, where the operator A can be noninvertible. Abstract results are applied to partial functional differential equations.

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