| Abstract: |
| Impulsive differential equations or inclusions describe phenomena characterized by the fact that the model parameters are subject to short-term perturbations in time. For instance, in the periodic treatment of some diseases, impulses may correspond to administration of a drug treatment; in environmental sciences, impulses may correspond to seasonal changes or harvesting; in economics, impulses may correspond to abrupt changes of prices. Typically, the moments of impulses are chosen to be fixed beforehand. However, the moments of impulses can be chosen in other ways, for instance, randomly, or determined by the state of a system, generating more interesting problems and more adherent to real life phenomena. In this talk will be presented some existence results for solutions of semilinear differential inclusions in Banach spaces with impulses at fixed or variable times moments. In particular, the linear part is assumed to be the generator of a non necessarily compact semigroup and Cauchy as well as nonlocal initial conditions will be considered, underlining the different set of hypotheses that are needed on the functions that determine the impulses in the two cases. |
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