Existence of positive periodic solutions for neutral functional differential equations with deviating arguments

2002 ◽  
Vol 17 (4) ◽  
pp. 382-390 ◽  
Author(s):  
Shiping Lu ◽  
Weigao Ge
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Neutral Functional Differential Equations ◽  
Deviating Arguments ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document