Positive periodic solutions of second-order nonlinear differential systems with two parameters
Positive periodic solutions of second-order nonlinear differential systems with two parameters
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DOI：
10.1016/j.camwa.2007.07.017
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发表时间：
2008-07
期刊：
影响因子：
--
通讯作者：
Jun Wu;Zhicheng Wang
中科院分区：
文献类型：
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作者：
Jun Wu;Zhicheng Wang
利用Deimling不动点指数理论，研究了一类具有两个参数（λ，μ）∈R+2 <${（0，0）}的二阶非线性微分系统.我们证明了R+2 <${（0，0）}存在三个非空子集：Γ，Δ 1和Δ 2，使得R+2 <${（0，0）}=Γ <$Δ1 <$Δ 2，并且当（λ，μ）∈Δ1时，系统至少有两个正周期解，当（λ，μ）∈Γ时，系统至少有一个正周期解，当（λ，μ）∈Δ2时，系统至少没有正周期解.同时，我们找到两条直线L1和L2，使得Γ位于L1和L2之间。
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, Δ1and Δ2such that R+2∖{(0,0)}=Γ∪Δ1∪Δ2and 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 L1and L2such that Γ lies between L1and L2.