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

 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”. PDF https://acadsol.eu/dsa/articles/26/34/13.pdf DOI 10.12732/dsa.v26i34.13 Refereed Designation Refereed