scholarly journals On the exact WKB analysis for the third order ordinary differential equations with a large parameter

1998 ◽  
Vol 2 (4) ◽  
pp. 625-640 ◽  
Author(s):  
Takashi Aoki ◽  
Takahiro Kawai ◽  
Yoshitsugu Takei
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Large Parameter ◽  
Third Order ◽  
The Third

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.

scholarly journals Linearizability of Nonlinear Third-Order Ordinary Differential Equations by Using a Generalized Linearizing Transformation

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
E. Thailert ◽  
S. Suksern
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Linear Equation ◽  
Ordinary Differential Equations ◽  
Third Order ◽  
Order Ordinary Differential Equation ◽  
The Third ◽  
Linearization Problem ◽  
Linearizable Equation

We discuss the linearization problem of third-order ordinary differential equation under the generalized linearizing transformation. We identify the form of the linearizable equations and the conditions which allow the third-order ordinary differential equation to be transformed into the simplest linear equation. We also illustrate how to construct the generalized linearizing transformation. Some examples of linearizable equation are provided to demonstrate our procedure.

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