Periodic solutions for generalized high-order neutral differential equation in the critical case

2009 ◽  
Vol 71 (12) ◽  
pp. 6182-6193 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Critical Case ◽  
High Order ◽  
Neutral Differential Equation

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.

scholarly journals Periodic solution for ϕ-Laplacian neutral differential equation

2019 ◽  
Vol 17 (1) ◽  
pp. 172-190 ◽  
Author(s):  
Shaowen Yao ◽  
Zhibo Cheng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
A Priori ◽  
Neutral Differential Equation ◽  
A Priori Bounds ◽  
T Tau

Abstract This paper is devoted to the existence of a periodic solution for ϕ-Laplacian neutral differential equation as follows $$\begin{array}{} (\phi(x(t)-cx(t-\tau))')'=f(t,x(t),x'(t)). \end{array}$$ By applications of an extension of Mawhin’s continuous theorem due to Ge and Ren, we obtain that given equation has at least one periodic solution. Meanwhile, the approaches to estimate a priori bounds of periodic solutions are different from the corresponding ones of the known literature.

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