scholarly journals NEW EXISTING RESULTS FOR A SYSTEM OF NONLINEAR THIRD-ORDER DIFFERENTIAL EQUATION VIA FIXED POINT INDEX

2018 ◽  
Vol 8 (6) ◽  
pp. 1694-1706
Author(s):  
Chengbo Zhai ◽  
◽  
Li Zhao ◽  
Shunyong Li ◽  
H. R. Marasi ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Index ◽  
Order Differential Equation ◽  
Point Index ◽  
Third Order ◽  
Third Order Differential Equation

scholarly journals Green’s Function and Positive Solutions of a Third-Order Equation with Periodic Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Nickolai Kosmatov
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Order Differential Equation ◽  
Periodic Boundary Conditions ◽  
Order Equation ◽  
Point Index ◽  
Third Order

We apply the fixed point index to obtain positive solutions of a nonresonant periodic boundary value problem for a third-order differential equation u‴+ρ3u=λfu.

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.

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.

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