Existence of resolvent for Volterra integral equations on time scales

Authors

  • Murat Adivar
  • Yousseff Raffoul

Keywords:

Existence, Resolvent, Shift operator, Time scales, Volterra integral equation

Abstract

This research is the first of its kind in which we introduce the shift operators and establish sufficient conditions for the existence of the resolvent for the Volterra integral equation $x(t)=f(t)+\int_{t_{0}}^{t}a(t,s)x(s)\Delta s$, for $t_{0}\i \mathbb{T}^{\kappa}$ on time scales. The paper will serve as the foundation for future research on the qualitative analysis of solutions of Volterra integral equation on time scale, using the notion of the resolvent. doi:10.1017/S0004972709001166

Published

2010-09-22

Issue

Vol. 82 (2010)

Section

Articles
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