Periodic solutions to superlinear indefinite planar systems: A topological degree approach

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 problem positive periodic second-order equations (involving linear or ϕ-Laplacian-type operators).