Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 170, pp. 1-8.
Title: Periodic solutions of neutral delay integral equations of advanced type
Authors: Muhammad N. Islam (Univ. of Dayton, Dayton, OH, USA)
Nasrin Sultana (Univ. of Dayton, Dayton, OH, USA)
James Booth (Univ. of Dayton, Dayton, OH, USA)
Abstract:
We study the existence of continuous periodic solutions
of a neutral delay integral equation of advanced type.
In the analysis we employ three fixed point theorems:
Banach, Krasnosel'skii, and Krasnosel'skii-Schaefer.
Krasnosel'skii-Schaefer fixed point theorem requires an
a priori bound on all solutions. We employ a Liapunov
type method to obtain such bound.
Submitted October 1, 2010. Published November 29, 2010.
Math Subject Classifications: 45D05, 45J05.
Key Words: Volterra integral equation; neutral delay integral equation;
periodic solution; Krasnosel'sii's fixed point theorem;
Schaefer's fixed point theorem; Liapunov's method.