Positive periodic solutions of second-order nonlinear differential systems with two parameters

By employing the Deimling fixed point index theory, we consider a class of second-order nonlinear differential systems with two parameters . We show that there exist three nonempty subsets of : Γ, Δ1 and Δ2 such that and the system has at least two positive periodic solutions for (λ,μ) Δ1, one positive periodic solution for (λ,μ) Γ and no positive periodic solutions for (λ,μ) Δ2. Meanwhile, we find two straight lines L1 and L2 such that Γ lies between L1 and L2.