Nonlinear variation of parameters and an application for integrodifferential equations with initial time difference

Abstract

The relationship between an unperturbed nonlinear integrodifferential system and a perturbed nonlinear integrodifferential system have been investigated that have different initial positions and an initial time difference (ITD). Variation of parameter techniques are employed to obtain analytical formulae and to define Lyapunov-like functions. A simple application of nonlinear variation of parameters formula is given to indicate its usefulness. Copyright © 2011 Watam Press. © 2012 Elsevier B.V., All rights reserved.