Existence of positive periodic solution for variable-coefficient third-order differential equation with singularity

2013 ◽  
Vol 37 (15) ◽  
pp. 2281-2289 ◽  
Author(s):  
Zhibo Cheng ◽  
Jingli Ren
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Third Order ◽  
Third Order Differential Equation

scholarly journals Multiplicity Results for Variable-Coefficient Singular Third-Order Differential Equation with a Parameter

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhibo Cheng ◽  
Yun Xin
Keyword(s):  
Differential Equation ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Positive Periodic Solutions ◽  
Third Order ◽  
Multiplicity Results ◽  
Third Order Differential Equation ◽  
Krasnoselskii Fixed Point Theorem

We investigate a class of variable coefficients singular third-order differential equation with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. By applications of Green’s function and the Krasnoselskii fixed point theorem, sufficient conditions for the existence of positive periodic solutions are established.

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.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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