Mathematics

In this talk I will present a recent joint work with Alberto Boscaggin (University of Torino) and Fabio Zanolin (University of Udine).We deal with the periodic problem associated with the indefinite differential equation u'' + q(t) g(u) = 0, where g(u) has superlinear growth at zero and sublinear growth at infinity.Using a topological technique based on Mawhin’s coincidence degree theory, we show how the number of positive solutions is affected by the nodal behavior of q(t). As a byproduct of our approach we also provide abundance of positive subharmonic solutions and symbolic dynamics.