TITLE:
Asymptotically Antiperiodic Solutions for a Nonlinear Differential Equation with Piecewise Constant Argument in a Banach Space
AUTHORS:
William Dimbour, Vincent Valmorin
KEYWORDS:
Asymptotically ω-Antiperiodic Functions, Differential Equations with Piecewise Constant Argument, Semi-Group
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.15,
September
16,
2016
ABSTRACT: In this paper, we give sufficient
conditions for the existence and uniqueness of asymptotically w-antiperiodic
solutions for a nonlinear differential equation with piecewise constant
argument in a Banach space when w is an integer.
This is done using the Banach fixed point theorem. An example involving the
heat operator is discussed as an illustration of the theory.