Maintenance of oscillatory and asymptotic behaviour of solutions of differential inequalities under the effect of advanced and mixed argument

1984 ◽  
Vol 44 (1-2) ◽  
pp. 21-33
Author(s):  
M. R. S. Kulenović
Keyword(s):  
Asymptotic Behaviour ◽  
Differential Inequalities ◽  
Asymptotic Behaviour Of Solutions ◽  
Mixed Argument

Asymptotic Behaviour of Solutions of Parabolic Differential Inequalities

1962 ◽  
Vol 14 ◽  
pp. 626-631 ◽  
Author(s):  
Milton Lees
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Asymptotic Behaviour ◽  
Differential Inequality ◽  
Second Order ◽  
Differential Inequalities ◽  
Order Linear ◽  
Open Set ◽  
Asymptotic Behaviour Of Solutions ◽  
Image Position

Let there be given a parabolic differential operatorwhere A is a second order linear elliptic (<0) differential operator in an open set Ω ⊂ Rn, having coefficients depending on x ∈ Ω and t ∈ [0, ∞]. Recently, Protter (1) investigated the asymptotic behaviour of functions u(x, t) that satisfy the differential inequality(1.1)Under suitable restrictions on the functions ci(t) and the coefficients of A, he proved that any solution of (1.1), subject to certain homogeneous boundary conditions, that vanishes sufficiently fast, as t → ∞, must be identically zero in Ω × [0, ∞). For example, conditions are given under which no solution of (1.1) can vanish faster than e-λt, ∀ λ > 0, unless identically zero.

On asymptotic behaviour of solutions of stochastic difference equations with volterra type main term

2000 ◽  
Vol 18 (5) ◽  
pp. 837-857 ◽  
Author(s):  
Alexandra Rodkina ◽  
Xuerong Mao ◽  
Vladimir Kolmanovskii
Keyword(s):  
Asymptotic Behaviour ◽  
Difference Equations ◽  
Main Term ◽  
Volterra Type ◽  
Stochastic Difference Equations ◽  
Asymptotic Behaviour Of Solutions
Sign in / Sign up

Export Citation Format

Share Document