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
1993 ◽  
Vol 08 (20) ◽  
pp. 3565-3576 ◽  
Author(s):  
L. A. IBORT ◽  
G. LANDI ◽  
J. MARÍN-SOLANO ◽  
G. MARMO

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.


Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 367
Author(s):  
Shyam Sundar Santra ◽  
Debasish Majumder ◽  
Rupak Bhattacharjee ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
...  

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.


1993 ◽  
Vol 113 (1) ◽  
pp. 205-224 ◽  
Author(s):  
Eduardo Martínez ◽  
José F. Cariñena ◽  
Willy Sarlet

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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