A general class of nonlinear impulsive integral differential equations and optimal controls on Banach spaces
The authors consider a quite general impulsive integral differential equation on a Banach space which may be infinite dimensional and prove the existence of a unique PWC-\(\alpha\)-mild solution by using a contraction map and a generalized Gronwall lemma. Furthermore, the existence of optimal controls of systems governed by impulsive integral differential equations is proved. Several conditions are stated which cannot be described shortly. An example is given which fulfills obviously the above given conditions.
scientific article; zbMATH DE number 5305505