scholarly journals ASYMPTOTIC REPRESENTATIONS OF SLOWLY VARYING SOLUTIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS WHICH HAS A RIGHT-HAND SIDE CONTAINING THE NONLINEARITIES OF DIFFERENT TYPES

2018 ◽  
Vol 6 (3-4) ◽  
pp. 89-102
Author(s):  
N. Kolun
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Right Hand ◽  
Different Types ◽  
Asymptotic Representations

Almost-conservative second-order differential equations

1975 ◽  
Vol 77 (1) ◽  
pp. 159-169 ◽  
Author(s):  
H. P. F. Swinnerton-Dyer
Keyword(s):  
Differential Equations ◽  
Rate Of Convergence ◽  
Second Order ◽  
Good Function ◽  
Second Order Differential Equations ◽  
Right Hand ◽  
Image Position ◽  
The Right

During the last thirty years an immense amount of research has been done on differential equations of the formwhere ε > 0 is small. It is usually assumed that the perturbing term on the right-hand side is a ‘good’ function of its arguments and that its dependence on t is purely trigonometric; this means that there is an expansion of the formwhere the ωn are constants, and that one may impose any conditions on the rate of convergence of the series which turn out to be convenient. Without loss of generality we can assumeand for convenience we shall sometimes write ω0 = 0. Often f is assumed to be periodic in t, in which case it is implicit that the period is independent of x and ẋ (We can also allow f to depend on ε, provided it does so in a sensible manner.)

Sliding solutions of second-order differential equations with discontinuous right-hand side

2017 ◽  
Vol 40 (14) ◽  
pp. 5295-5306 ◽  
Author(s):  
Clayton E. L. da Silva ◽  
Paulo R. da Silva ◽  
Alain Jacquemard
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Right Hand
Sign in / Sign up

Export Citation Format

Share Document