Construction of asymptotic solutions for quasilinear third-order differential equations with lag

1984 ◽  
Vol 35 (3) ◽  
pp. 342-346
Author(s):  
Chan Kim T'i
Keyword(s):  
Differential Equations ◽  
Asymptotic Solutions ◽  
Third Order

Asymptotic theory for third-order differential equations with extension to higher odd-order equations

1991 ◽  
Vol 117 (3-4) ◽  
pp. 215-223 ◽  
Author(s):  
A. S. A. Al-Hammadi
Keyword(s):  
Differential Equations ◽  
Asymptotic Theory ◽  
Order Theory ◽  
Linear Differential Equations ◽  
Asymptotic Solutions ◽  
Third Order ◽  
Odd Order ◽  
Linear Differential ◽  
General Conditions

SynopsisAn asymptotic theory is developed for linear differential equations of odd order. Theory is applied with large coefficients. The forms of the asymptotic solutions are given under general conditions on the coefficients.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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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