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

✍ Scribed by Jun Wu; Zhicheng Wang

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 282 KB
• Volume: 56
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2007.07.017

✦ Synopsis

By 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 , ∆ 1 and ∆ 2 such that R 2 + \ {(0, 0)} = Γ ∪ ∆ 1 ∪ ∆ 2 and the system has at least two positive periodic solutions for (λ, µ) ∈ ∆ 1 , one positive periodic solution for (λ, µ) ∈ Γ and no positive periodic solutions for (λ, µ) ∈ ∆ 2 . Meanwhile, we find two straight lines L 1 and L 2 such that Γ lies between L 1 and L 2 .