TY - JOUR
T1 - Positive Periodic Solutions of Systems of First Order Ordinary Differential Equations
AU - O’Regan, Donal
AU - Wang, Haiyan
N1 - Publisher Copyright:
© 2005, Birkhäuser Verlag, Basel.
PY - 2005/11/1
Y1 - 2005/11/1
N2 - Consider the n-dimensional nonautonomous system ẋ(t) = A(t)G(x(t)) − B(t)F(x(t − τ(t))) Let u = (u1,…,un),(Formula Presented.). Under some quite general conditions, we prove that either F0 = 0 and F∞ = ∞, or F0 = ∞ and F∞ = 0, guarantee the existence of positive periodic solutions for the system for all λ > 0. Furthermore, we show that F0 = F∞ = 0, or F∞ = F∞ = ∞ guarantee the multiplicity of positive periodic solutions for the system for sufficiently large, or small λ, respectively. We also establish the nonexistence of the system when either F0 and F∞ > 0, or F0 and F∞, < for sufficiently large, or small λ, respectively. We shall use fixed point theorems in a cone.
AB - Consider the n-dimensional nonautonomous system ẋ(t) = A(t)G(x(t)) − B(t)F(x(t − τ(t))) Let u = (u1,…,un),(Formula Presented.). Under some quite general conditions, we prove that either F0 = 0 and F∞ = ∞, or F0 = ∞ and F∞ = 0, guarantee the existence of positive periodic solutions for the system for all λ > 0. Furthermore, we show that F0 = F∞ = 0, or F∞ = F∞ = ∞ guarantee the multiplicity of positive periodic solutions for the system for sufficiently large, or small λ, respectively. We also establish the nonexistence of the system when either F0 and F∞ > 0, or F0 and F∞, < for sufficiently large, or small λ, respectively. We shall use fixed point theorems in a cone.
KW - existence
KW - fixed point theorem
KW - positive periodic solutions
UR - https://www.scopus.com/pages/publications/34249319507
U2 - 10.1007/BF03323371
DO - 10.1007/BF03323371
M3 - Article
SN - 1422-6383
VL - 48
SP - 310
EP - 325
JO - Results in Mathematics
JF - Results in Mathematics
IS - 3-4
ER -