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DEMONSTRATE MATHEMATICAVol. XXXIVNo 42001M. Benchohra, S. K. NtouyasEXISTENCE RESULTS ON SEMIINFINITEINTERVALS FOR FUNCTIONAL-DIFFERENTIALA N D INTEGRODIFFERENTIAL INCLUSIONSIN B A N A C H SPACES WITH NONLOCAL CONDITIONS1. IntroductionIn this paper we study the existence of mild solutions, defined on asemi-infinite interval, for initial value problem (IVP for short) for first orderfunctional-differential and integrodifferential inclusions together with nonlocal conditions. In Section 3 we consider the following IVP:(1)(2)y' - Ay G F{t,yt),a . e . t e J = [0, o o ) ,! / ( 0 + ( / ( » * „ . . . , I/t p ))(i) = 0(<),te[-r,0],where F : J x C([—r, 0], E) —> 2E is a bounded, closed, convex multivaluedmap, <f> E C([-r,0],£), 0 < h < ... < tp < oo, p € N, / : [C([-r,0],£)] p ^C([—r, 0], JS7), A is a linear closed operator from a dense subspace D(A) ofE into E and E is a real Banach space with the norm | • |.For any continuous function y, defined on the interval [—r, oo), and anyt e J, we denote by yt the element of C([—r, 0], E), defined byyt(0) = y(t + 9),0G[-r,O],Here, yt(-) represents the history
Demonstratio Mathematica – de Gruyter
Published: Oct 1, 2001
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