Existence results for impulsive neutral evolution integrodifferential equations with infinite delay
Integrodifferential equations are encountered in many areas of science, where it is necessary to take into account aftereffect or delay (for example, in control theory, biology, ecology and medicine). Especially, one always describes a model which possesses hereditary properties by integrodifferential equations in practice. The theory of integrodifferential equations with impulse actions has not yet been fully investigated, when compared to that of impulsive differential equations and integrodifferential equations. Recently neutral impulsive differential and integrodifferential equations have received considerable interest from researchers. In this paper, the authors prove the existence of mild solutions for impulsive neutral evolution integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using the analytic semigroup theory and the Krasnoselski-Schaefer type fixed point theorem. An example is provided to illustrate the theory.
impulsive neutral evolution integrodifferential equations
Krasnoselski-Schaefer type fixed point theorem
scientific article; zbMATH DE number 5632681
scientific article