Title

Nonlinear Integrodifferential Equations and A Priori Bounds on Periodic Solutions

Author(s)

Muhammad Islam, University of DaytonFollow
T. A. Burton, Southern Illinois University Carbondale
Paul W. Eloe (0000-0002-6590-9931), University of DaytonFollow

Document Type

Article

Publication Date

12-1992

Publication Source

Annali di Matematica Pura ed Applicata

Abstract

This paper studies the existence of aperiodic solution of a nonlinear integrodifferential system of the form x′(t)=Dx(t)+f(x(t))+^t∫_−∞k(t,s)g(x(s))ds+p(t), for each continuous periodic function p and under suitable assumptions on f, k and g. A topological transversality method is employed to obtain the existence of periodic solutions. This method relies on a priori bounds on periodic solutions. Several examples are provided where a variant of Liapunov's direct method is employed to obtain a priori bounds on periodic solutions.

Inclusive pages

271-283

ISBN/ISSN

0373-3114

Comments

The document available for download is the authors' accepted manuscript, provided in compliance with the publisher's policy on self-archiving. To read the version of record, use the DOI provided.

Permission documentation on file.

Copyright

Copyright © 1992, Fondazione Annali di Matematica Pura ed Applicata

Publisher

Springer Berlin Heidelberg

Volume

161

Issue

1

Place of Publication

Italy

Peer Reviewed

yes

eCommons Citation

Islam, Muhammad; Burton, T. A.; and Eloe, Paul W., "Nonlinear Integrodifferential Equations and A Priori Bounds on Periodic Solutions" (1992). Mathematics Faculty Publications. 47.
https://ecommons.udayton.edu/mth_fac_pub/47