Existence of solutions on compact and non-compact intervals for semilinear impulsive differential inclusions with delay

Irene Benedetti, Paola Rubbioni

DOI: http://dx.doi.org/10.12775/TMNA.2008.047

Abstract


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.

Keywords


Semilinear differential inclusions; impulsive Cauchy problems; delay differential inclusions; mild solutions; condensing multifunctions

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