scholarly journals Asymptotic theory for a critical class of third-order differential equations

2020 ◽  
Vol 44 (6) ◽  
pp. 2147-2154
Author(s):  
Aziz S. A. AL-HAMMADI
Keyword(s):  
Differential Equations ◽  
Asymptotic Theory ◽  
Third Order ◽  
Critical Class

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.

Asymptotic theory for a critical class of fourth-order differential equations

1982 ◽  
Vol 383 (1785) ◽  
pp. 465-476 ◽  
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Critical Case ◽  
Asymptotic Theory ◽  
All Solutions ◽  
Exponential Character ◽  
Independent Variable ◽  
Fourth Order Equations ◽  
Critical Class ◽  
Asymptotic Forms

A recently formulated asymptotic theory for differential equations with large coefficients that are like powers of the independent variable is developed here for fourth-order equations with general coefficients. In this general approach a critical case is identified that forms a borderline between situations where all solutions have asymptotically a certain exponential character in terms of the coefficients and where only two solutions have this character. The asymptotic forms of a fundamental set of solutions are obtained in the critical case.

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.

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