scholarly journals Symmetry analysis of a class of autonomous even-order ordinary differential equations

2015 ◽  
Vol 80 (6) ◽  
pp. 1739-1758 ◽  
Author(s):  
P. L. da Silva ◽  
I. L. Freire
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Symmetry Analysis ◽  
Even Order

A nonlocal problem for a differential operator of even order with involution

2020 ◽  
Vol 26 (2) ◽  
pp. 297-307
Author(s):  
Petro I. Kalenyuk ◽  
Yaroslav O. Baranetskij ◽  
Lubov I. Kolyasa
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Riesz Basis ◽  
Existence And Uniqueness ◽  
Spectral Properties ◽  
Nonlocal Problem ◽  
Even Order

AbstractWe study a nonlocal problem for ordinary differential equations of {2n}-order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.

scholarly journals Symbolic Implementation of Preliminary Group Classiffication for Ordinary Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
K. S. Govinder
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Group Classification ◽  
Symmetry Analysis ◽  
Analysis Package ◽  
Small File ◽  
Fowler Equation ◽  
Preliminary Group

We apply the method of preliminary group classification to ordinary differential equations of the formy(n)=E(x,y,y',…,y(n-1),fi(x)),  i=0,…,m.We show how this method can be implemented via the popular symmetry analysis packagePROGRAM LIEprovided that the package is supplemented with a small file. We then apply this method to an extension of the generalised Emden-Fowler equation given byy′′=∑i=25fixyi.

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