Positive periodic solutions of functional differential equations
Positive periodic solutions of functional differential equations
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DOI：
10.1016/j.jde.2004.02.018
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发表时间：
2004-08
影响因子：
2.4
通讯作者：
Haiyan Wang
中科院分区：
文献类型：
--
作者：
Haiyan Wang
We consider the existence, multiplicity and nonexistence of positive ω-periodic solutions for the periodic equation x′(t)=a(t)g(x)x(t)−λb(t)f(x(t−τ(t))), where a,b∈C( R ,[0,∞)) are ω-periodic, ∫ 0 ω a(t) dt>0 , ∫ 0 ω b(t) dt>0 , f,g∈C([0,∞),[0,∞)), and f(u)>0 for u>0, g(x) is bounded, τ(t) is a continuous ω-periodic function. Define f0= limu→0+f(u) u , f∞= limu→∞f(u) u , i0=number of zeros in the set { f0,f∞} and i∞=number of infinities in the set { f0,f∞} . We show that the equation has i0or i∞positive ω-periodic solution(s) for sufficiently large or small λ>0, respectively.
