Existence of positive periodic solutions for neutral functional differential equations

2007 ◽  
Vol 66 (1) ◽  
pp. 253-267 ◽  
Author(s):  
Guirong Liu ◽  
Jurang Yan ◽  
Fengqin Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Neutral Functional Differential Equations ◽  
Functional Differential

Positive periodic solutions for singular high-order neutral functional differential equations

2018 ◽  
Vol 68 (2) ◽  
pp. 379-396 ◽  
Author(s):  
Fanchao Kong ◽  
Zhiguo Luo ◽  
Shiping Lu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
High Order ◽  
Positive Periodic Solutions ◽  
Neutral Functional Differential Equation ◽  
Neutral Functional Differential Equations ◽  
Small Force ◽  
Functional Differential

Abstract In this paper, we establish new results on the existence of positive periodic solutions for the following high-order neutral functional differential equation (NFDE) $$\begin{array}{} (x(t)-cx(t-\sigma)) ^{(2m)}+f(x(t)) x'(t)+g(t,x(t-\delta))=e(t). \end{array}$$ The interesting thing is that g has a strong singularity at x = 0 and satisfies a small force condition at x = ∞, which is different from the corresponding ones known in the literature. Two examples are given to illustrate the effectiveness of our results.

Existence of positive periodic solutions of fourth-order singular p-Laplacian neutral functional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5855-5868 ◽  
Author(s):  
Fanchao Kong ◽  
Shiping Lu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Neutral Functional Differential Equations ◽  
Time Varying Delay ◽  
Functional Differential

This work deals with the existence of positive periodic solutions for the fourth-order p-Laplacian neutral functional differential equations with a time-varying delay and a singularity. The results are established using the continuation theorem of coincidence degree theory and some analysis methods. A numerical example is presented to illustrate the effectiveness and feasibility of the proposed criterion.

scholarly journals Positive Periodic Solutions for First-Order Neutral Functional Differential Equations with Periodic Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Zeqing Liu ◽  
Xin Li ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Neutral Functional Differential Equations ◽  
First Order ◽  
Krasnoselskii Fixed Point Theorem ◽  
Functional Differential ◽  
Periodic Delays

In this paper, two classes of first-order neutral functional differential equations with periodic delays are considered. Some results on the existence of positive periodic solutions for the equations are obtained by using the Krasnoselskii fixed point theorem. Four examples are included to illustrate our results.

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