scholarly journals On the existence and multiplicity of positive periodic solutions for first-order vector differential equation

2007 ◽  
Vol 329 (2) ◽  
pp. 977-986
Author(s):  
Xiao Han ◽  
Shuguan Ji ◽  
Zhonghua Ma
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
First Order ◽  
Existence And Multiplicity ◽  
Vector Differential Equation

scholarly journals On Positive Periodic Solutions to Nonlinear Fifth-Order Differential Equations with Six Parameters

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Yunhai Wang ◽  
Fanglei Wang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Function ◽  
Periodic Solutions ◽  
Positive Periodic Solutions ◽  
Existence And Multiplicity ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fifth Order

We study the existence and multiplicity of positive periodic solutions to the nonlinear differential equation:u5(t)+ku4(t)-βu3-ξu″(t)+αu'(t)+ωu(t)=λh(t)f(u),  in  0≤t≤1,  ui(0)=ui(1),  i=0,1,2,3,4, wherek,α,ω,λ>0,  β,ξ∈R,h∈C(R,R)is a 1-periodic function. The proof is based on the Krasnoselskii fixed point theorem.

scholarly journals Existence and Lyapunov Stability of Positive Periodic Solutions for a Third-Order Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Yueli Chen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Lyapunov Stability ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Positive Periodic Solutions ◽  
Third Order

By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.

Multiple periodic solutions for system of first-order differential equation

2009 ◽  
Vol 88 (7) ◽  
pp. 1005-1014 ◽  
Author(s):  
Seshadev Padhi ◽  
Smita Pati
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
First Order ◽  
Multiple Periodic Solutions

scholarly journals Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Mustafa Hasanbulli ◽  
Svitlana P. Rogovchenko ◽  
Yuriy V. Rogovchenko
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Blow Up ◽  
Single Species ◽  
Bifurcation Parameter ◽  
Positive Periodic Solutions ◽  
Large Initial Data ◽  
Fluctuating Environment ◽  
Species Population ◽  
Single Species Population

We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameterσassociated with the intensity of harvesting is explored. Asσgrows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically.

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