, Volume 185, Issue 3, pp 437-460

Existence and stability in the α-norm for partial functional differential equations of neutral type

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Abstract

In this work, we study a general class of partial neutral functional differential equations. We assume that the linear part generates an analytic semigroup and the nonlinear part is Lipschitz continuous with respect to the é-norm associated to the linear part. We discuss the existence, uniqueness, regularity and stability of solutions. Our results are illustrated by an example. This work extends previous results on partial functional differential equations (Fitzgibbon and Parrot, Nonlinear Anal., TMA 16, 479–487 (1991), Hale, Rev. Roum. Math. Pures Appl. 39, 339–344 (1994), Hale, Resen. Inst. Mat. Estat. Univ. Sao Paulo 1, 441–457 (1994), Travis and Webb, Trans. Am. Math. Soc. 240 129–143 (1978), Wu and Xia, J. Differ. Equ. 124 247–278 (1996)).

Mathematics Subject Classification (1991) 34K20, 34K30, 34K40, 47D06