Positive Periodic Solutions of Third-Order Ordinary Differential Equations with Delays
Yongxiang Li,Qiang Li +1 more
TLDR
In this article, the existence results of positive -periodic solutions are obtained for the third-order ordinary differential equation with delays where is - periodic function and is a continuous function which is - Periodic in are positive constants.Abstract:
The existence results of positive -periodic solutions are obtained for the third-order ordinary differential equation with delays where is -periodic function and is a continuous function which is -periodic in are positive constants. The discussion is based on the fixed-point index theory in cones.read more
Citations
More filters
Journal ArticleDOI
Green’s Function and Positive Solutions of a Third-Order Equation with Periodic Boundary Conditions
TL;DR: In this paper, the fixed point index was applied to obtain positive solutions of a nonresonant periodic boundary value problem for a third-order differential equation, which is a special case of the periodic boundary values problem.
References
More filters
Journal ArticleDOI
The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher Order Boundary Value Problems
TL;DR: In this paper, the authors developed the monotone method in the presence of lower and upper solutions for the problem u (n) (t)=ƒ(t, u(t));u (i) (a)−u(i)(b)=λ i ∈ R ; i=0,..., n−1.
Journal ArticleDOI
Periodic solutions of single-species models with periodic delay
H. I. Freedman,Jianhong Wu +1 more
TL;DR: In this article, a single-species population growth model is considered, where the growth rate response to changes in its density has a periodic delay, and if the self-inhibition rate is sufficiently large compared to the reproduction rate, then the model equation has a globally asymptotically stable positive periodic solution.
Journal ArticleDOI
A new existence theory for positive periodic solutions to functional differential equations
TL;DR: In this paper, a new existence theory for positive periodic solutions to a kind of non-autonomous functional differential equation by employing the fixed-point theorem in cones was proposed, which was applied to several biomathematical models.
Journal ArticleDOI
Remarks on the lower and upper solutions method for second- and third-order periodic boundary value problems
TL;DR: In this article, the solvability and the approximation of the solutions by monotone iteration of the second-and third-order periodic boundary value problems (BVPs) were studied.
Journal ArticleDOI
The method of lower and upper solutions for third-order periodic boundary value problems
TL;DR: In this paper, the monotone method in the presence of lower and upper solutions for the problem L n u(t) = ƒ(t,u(t)); u(i) (0) − u (i)(2π) = μ i ∈ R ; i = 0,..., n − 1, with Ln an nth-order linear operator and ǫ a Caratheodory function, was developed.