Existence results for first and second order semilinear impulsive differential inclusions
The authors prove several results on existence of solutions to impulsive semilinear differential inclusions in a real separable Banach space. In each case, the existence of a maximal solution to an associated problem is assumed, and the result is obtained by using a fixed-point approach based on Leray-Schauder's alternative theorem. First- and second-order problems are studied, including functional-differential inclusions. Both upper- and lower-semicontinuous cases are considered. The authors note that several of these theorems are new even for the non-impulsive case.
scientific article; zbMATH DE number 5001926