IMPACT OSCILLATORS OF HILL'S TYPE WITH INDEFINITE WEIGHT: PERIODIC AND CHAOTIC DYNAMICS

摘要

We prove the existence of globally defined bouncing solutions with prescribed number of impacts in the intervals of negativity and positivity of q. Furthermore, we show that when q is periodic, the equation under consideration exhibits an interesting phenomenon of chaotic-like dynamics. Finally, in case that q is even and periodic, we prove the existence and multiplicity of the even and periodic bouncing solutions for the Hill's type equation in case of f ≡ 0.