Title | THE AMBROSETTI-PRODI PERIODIC PROBLEM: DIFFERENT ROUTES TO COMPLEX DYNAMICS |
Publication Type | Journal Article |
Year of Publication | 2017 |
Authors | SOVRANO ELISA, ZANOLIN FABIO |
Journal | Dynamic Systems and Applications |
Volume | 26 |
Issue | 3&4 |
Start Page | 589 |
Pagination | 38 |
Date Published | 2017 |
ISSN | 1056-2176 |
AMS Subject Classification | 34C25, 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”. |
https://acadsol.eu/dsa/articles/26/34/13.pdf | |
DOI | 10.12732/dsa.v26i34.13 |
Refereed Designation | Refereed |