scholarly journals Necessary and Sufficient Conditions for the Oscillation of Forced Nonlinear Second Order Differential Equations with Delayed Argument

1997 ◽  
Vol 212 (1) ◽  
pp. 51-59 ◽  
Author(s):  
A.H. Nasr
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Second Order Differential Equations ◽  
Delayed Argument ◽  
Necessary And Sufficient

ON THE INVERSE PROBLEM OF LAGRANGIAN SUPERMECHANICS

1993 ◽  
Vol 08 (20) ◽  
pp. 3565-3576 ◽  
Author(s):  
L. A. IBORT ◽  
G. LANDI ◽  
J. MARÍN-SOLANO ◽  
G. MARMO
Keyword(s):  
Inverse Problem ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Lagrangian Function ◽  
Necessary And Sufficient Conditions ◽  
Recursion Operators ◽  
Second Order Differential Equations ◽  
Necessary And Sufficient

The inverse problem of Lagrangian supermechanics is investigated. A set of necessary and sufficient conditions for a system of second order differential equations in superspace to derive from a (possibly nonregular) super-Lagrangian function are given. The harmonic superoscillator is revisited and a family of even and odd alternative super-Lagrangians are constructed for it. Finally, we comment on the existence of recursion operators.

scholarly journals New Theorems for Oscillations to Differential Equations with Mixed Delays

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 367
Author(s):  
Shyam Sundar Santra ◽  
Debasish Majumder ◽  
Rupak Bhattacharjee ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
...  
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Mixed Delays ◽  
Second Order Differential Equations ◽  
Neutral Term ◽  
The Right ◽  
Necessary And Sufficient

The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form p(ι)w′(ι)α′+r(ι)uβ(ν(ι))=0,ι≥ι0 where w(ι)=u(ι)+q(ι)u(ζ(ι)). Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

Geometric characterization of separable second-order differential equations

1993 ◽  
Vol 113 (1) ◽  
pp. 205-224 ◽  
Author(s):  
Eduardo Martínez ◽  
José F. Cariñena ◽  
Willy Sarlet
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Geometric Characterization ◽  
One Dimensional ◽  
Practical Procedure ◽  
Second Order Differential Equations ◽  
Necessary And Sufficient ◽  
Second Order Equations

AbstractWe establish necessary and sufficient conditions for the separability of a system of second-order differential equations into independent one-dimensional second-order equations. The characterization of this property is given in terms of geometrical objects which are directly related to the system and relatively easy to compute. The proof of the main theorem is constructive and thus yields a practical procedure for constructing coordinates in which the system decouples.

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