EXISTENCE OF ASYMPTOTICALLY ω-ANTIPERIODIC MILD SOLUTIONS FOR SOME DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT AND NONDENSE DOMAIN
In this paper, we investigate the existence of asymptotically ω-antiperiodic mild solutions for some differential equations with piecewise constant argument and nondense domain in a Banach space when the perturbation term takes their value in the extrapolated space and ω is an integer. Our analysis is based on the extrapolation methods, theory of a strongly continuous semigroup of operators and the Banach contraction mapping principle.
mild solution, asymptotically ω-antiperiodic, differential equations with piecewise constant argument, nondense domain, semigroup operator, Banach fixed point theorem.