Nonlinear Integrodifferential Equations and A Priori Bounds on Periodic Solutions
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
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
COinS
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.