TY - JOUR
T1 - Positive periodic solutions of functional differential equations
AU - Wang, Haiyan
N1 - Copyright:
Copyright 2004 Elsevier B.V., All rights reserved.
PY - 2004/8/1
Y1 - 2004/8/1
N2 - 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, ∫0ω a(t) dt>0, ∫0ωb(t) 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 i0 or i∞ positive ω-periodic solution(s) for sufficiently large or small λ>0, respectively.
AB - 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, ∫0ω a(t) dt>0, ∫0ωb(t) 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 i0 or i∞ positive ω-periodic solution(s) for sufficiently large or small λ>0, respectively.
KW - Existence
KW - Fixed index theorem
KW - Multiplicity
KW - Nonexistence
KW - Positive periodic solution
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U2 - 10.1016/j.jde.2004.02.018
DO - 10.1016/j.jde.2004.02.018
M3 - Article
AN - SCOPUS:3543075159
VL - 202
SP - 354
EP - 366
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 2
ER -