THE AMBROSETTI-PRODI PERIODIC PROBLEM: DIFFERENT ROUTES TO COMPLEX DYNAMICS

TitleTHE AMBROSETTI-PRODI PERIODIC PROBLEM: DIFFERENT ROUTES TO COMPLEX DYNAMICS
Publication TypeJournal Article
Year of Publication2017
AuthorsSOVRANO ELISA, ZANOLIN FABIO
JournalDynamic Systems and Applications
Volume26
Issue3&4
Start Page589
Pagination38
Date Published2017
ISSN1056-2176
AMS Subject Classification34C25, 34C28, 37G20, 54H20
Abstract

We consider a second order nonlinear ordinary differential equation of the form ${ u′′+ f(u) = p(t)}$  where the forcing term ${p(t)}$ is a ${T}$ -periodic function and the nonlinearity ${ f(u) }$ satisfies properties related to problems of Ambrosetti-Prodi type. We discuss the existence of infinitely many periodic solutions as well as the presence of complex dynamics under different conditions on ${ p(t) }$ and by using different kinds of approaches. On the one hand, we exploit the Melnikov’s method and, on the other hand, the concept of “topological horseshoe”.

PDFhttps://acadsol.eu/dsa/articles/26/34/13.pdf
DOI10.12732/dsa.v26i34.13
Refereed DesignationRefereed