Electron. J. Diff. Equ., Vol. 2010(2010), No. 170, pp. 1-8.

Periodic solutions of neutral delay integral equations of advanced type

Muhammad N. Islam, Nasrin Sultana, James Booth

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.

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Muhammad N. Islam
Department of Mathematics, University of Dayton
Dayton, OH 45469-2316 USA
email: muhammad.islam@notes.udayton.edu
Nasrin Sultana
Department of Mathematics, University of Dayton
Dayton, OH 45469-2316 USA
email: sultannz@notes.udayton.edu
James Booth
Department of Mathematics, University of Dayton
Dayton, OH 45469-2316 USA
email: boothjaa@notes.udayton.edu

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