scholarly journals Positive periodic solution of first-order neutral differential equation with infinite distributed delay and applications

2020 ◽  
Vol 5 (6) ◽  
pp. 7372-7386
Author(s):  
Zhibo Cheng ◽  
◽  
Lisha Lv ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Distributed Delay ◽  
Positive Periodic Solution ◽  
Neutral Differential Equation ◽  
First Order

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

scholarly journals Strong singularities of attractive and repulsive type to 2n-order neutral differential equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yun Xin ◽  
Shaowen Yao ◽  
Ruichen Wang
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Nonlinear Term ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solution ◽  
Neutral Differential Equation ◽  
Coincidence Degree Theory

Abstract This paper is devoted to the existence of a positive periodic solution for a kind of 2n-order neutral differential equation with a singularity, where nonlinear term $g(t,x)$ g ( t , x ) has strong singularities of attractive and repulsive type at the origin. Our proof is based on coincidence degree theory.

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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