Existence and stability in the α-norm for partial functional differential equations of neutral type |
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| Authors: | Mostafa Adimy Khalil Ezzinbi |
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| Institution: | (1) Laboratoire de Mathématiques Appliquées, I.P.R.A., FRE 2570, Université de Pau, Avenue de l’université, 64000 Pau, France;(2) Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakesh, Morocco |
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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 |
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| Keywords: | Partial functional differential equations Analytic semigroup Fractional power Mild solution Characteristic value Stability |
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