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

Authors:	Jun Wu Zhicheng Wang

Affiliation:	^aCollege of Mathematics, Changsha University of Science Technology, Changsha, 410076, China ^bCollege of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

Abstract:	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.

Keywords:	Positive periodic solutions Second-order differential system Fixed point theorem Fixed point index Nonlinear systems
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