We show that, for a certain class of systems, the problem of establishing the existence of periodic orbits can be successfully studied by means of a symbolic dynamics approach combined with interval methods. Symbolic dynamics is used to find approximate positions of periodic points, and the existence of periodic orbits in a neighborhood of these approximations is proved using an interval operat...

We deal with a planar differential system of the form{u′=h(t,v),v′=−λa(t)g(u), where h is T-periodic in first variable and strictly increasing second variable, λ>0, sign-changing weight function g superlinear. Based on coincidence degree theory, dependence λ, we prove existence solutions (u,v) such that u(t)>0 for all t∈R. Our results generalize unify previous contributions about Butler's probl...

We present here results about the existence of periodic orbits for projected dynamical systems (PDS) under Minty-Browder monotonicity conditions. The results are formulated in the general context of a Hilbert space of arbitrary (finite or infinite) dimension. The existence of periodic orbits for such PDS is deduced by means of nonlinear analysis, using a fixed point approach. It is also shown h...