Existence of solutions on compact and non-compact intervals for semilinear impulsive differential inclusions with delay
Keywords
Semilinear differential inclusions, impulsive Cauchy problems, delay differential inclusions, mild solutions, condensing multifunctionsAbstract
In this paper we deal with impulsive Cauchy problems in Banach spaces governed by a delay semilinear differential inclusion $y'\in A(t)y$ $ + F(t,y_t)$. The family $\{A(t)\}_{t\in [0,b]}$ of linear operators is supposed to generate an evolution operator and $F$ is a upper Carath\`eodory type multifunction. We first provide the existence of mild solutions on a compact interval and the compactness of the solution set. Then we apply this result to obtain the existence of mild solutions for the impulsive Cauchy problem on non-compact intervals.Downloads
Published
2008-12-01
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1.
BENEDETTI, Irene and RUBBIONI, Paola. Existence of solutions on compact and non-compact intervals for semilinear impulsive differential inclusions with delay. Topological Methods in Nonlinear Analysis. Online. 1 December 2008. Vol. 32, no. 2, pp. 227 - 245. [Accessed 23 April 2024].
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