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

Abstract

AbstractBy employing the Deimling fixed point index theory, we consider a class of second-order nonlinear differential systems with two parameters (λ,μ)∈R+2∖{(0,0)}. We show that there exist three nonempty subsets of R+2∖{(0,0)}: Γ, Δ1 and Δ2 such that R+2∖{(0,0)}=Γ∪Δ1∪Δ2 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