T-periodic solutions for a second order system with singular nonlinearity

Abstract

We consider a system of the form u’' + au’ = Hv(u, v)-h(t) v’' + bv’ = Hu(u, v)-k(t), where h, k are locally integrable and T-periodic, and H is a C1 function defined on (0,∞)x(0,∞), for which a good model is given by H(u, v) =-(1/uα + 1/vβ),α,β, > 0. We state conditions under which existence of positive, T-periodic solutions for this system is ensured. We also study the problems of uniqueness and existence of multiple solutions in some special cases. © 1995, Khayyam Publishing.