Existence of Solutions for Nonlinear Evolution Equations With Infinite Delay

Abstract

Abstract. This paper is concerned with nonlinear evolution differential equations with infinite delay in Banach spaces. Using Kato's approximating approach, existence and uniqueness of strong solutions are obtained.

Approximate Controllability for a Semilinear Evolution System with Infinite Delay

“…A variety of mathematical models for physical, chemical, or biological processes are most appreciatively formed as PFDEs with infinite delay, for example the reaction-diffusion logistic equation with infinite delay and equations of heat conduction in materials with fading memory. In the past decades, existence, uniqueness, periodicity, regularity, and stability of the solutions for this kind of evolution equations have been studied by many authors, see [1,2,5,10,11,23,24] among others, and see [12,25] for more practical background of this kind of equations.…”