Asypmtotic Behavior of Nonlinear Functional Evolution Equations in Fading Memory Spaces

Abstract

Publisher Summary This chapter analyzes asypmtotic behavior of nonlinear functional evolution equations in fading memory spaces, and discusses about Banach space and abstract nonlinear functional differential equations involving infinite delay. The chapter attempts to obtain an asymptotic convergence result for solutions to some specific equation. The integral comparison technique of Redlinger is adapted from the case of semilinear finite delay equations to nonlinear infinite delay. The chapter opines that the Redlinger technique will prove to be a useful tool for nonlinear evolution equations. Following the Redlinger technique, the chapter introduces the scalar integral operator S . The chapter further discusses a comparison principle as a modification of a lemma of Redlinger.