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Viability for semilinear differential equations of retarded type

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Abstract

LetX be a Banach space, A :D(A) X ! X the generatorof a compact C0-semigroup S(t) :X ! X;t 0,D a locally closed subsetin X , and f : (a;b) C([ q;0];X ) ! X a function of Caratheodory type.The main result of this paper is that a necessary and sucient conditionin order that D be a viable domain of the semilinear dierential equationof retarded typeu0(t) = Au(t) + f(t;ut);t2 [t0;t0 + T];ut0 = 2 C([ q;0];X )is the tangency conditionliminfh #0h1d(S(h)v(0) + hf (t;v);D) = 0for almost everyt2 (a;b) and every v 2 C([ q;0];X ) with v(0)2 D.

참고문헌 (18)

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