Some applications of functional-differential inequalities

1987 ◽  
Vol 38 (6) ◽  
pp. 658-661
Author(s):  
D. A. Vzovskii
Keyword(s):  
Differential Inequalities ◽  
Functional Differential

scholarly journals Functional Differential Inequalities with Unbounded Delay

2005 ◽  
Vol 12 (2) ◽  
pp. 237-254
Author(s):  
Zdzisław Kamont ◽  
Adam Nadolski
Keyword(s):  
Differential Inequality ◽  
Continuous Dependence ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Classical Solutions ◽  
Differential Inequalities ◽  
Unbounded Delay ◽  
Several Variables ◽  
Functional Differential ◽  
Continuous Dependence Of Solutions

Abstract We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perron-type uniqueness result and a result on continuous dependence of solutions on given functions for partial functional differential equations with unbounded delay. We consider classical solutions on the Haar pyramid.

Oscillatory and asymptotic properties of a class of operator-differential inequalities

1984 ◽  
Vol 96 (1-2) ◽  
pp. 5-13 ◽  
Author(s):  
A. D. Myshkis ◽  
D. D. Bainov ◽  
A. I. Zahariev
Keyword(s):  
Asymptotic Behaviour ◽  
Asymptotic Properties ◽  
Neutral Type ◽  
Differential Inequalities ◽  
Functional Differential ◽  
Image Position ◽  
Oscillatory Properties

SynopsisThe present paper studies some asymptotic (including oscillatory) properties of the solutions of operator-differential inequalities of the formwhere(the latter symbol denotes the space of locally summable functions).As an application of the results obtained, theorems are proved for the asymptotic behaviour of the solutions of certain classes of functional-differential and integro-differential neutral-type equations.

scholarly journals A system of impulsive degenerate nonlinear parabolic functional-differential inequalities

1995 ◽  
Vol 8 (1) ◽  
pp. 59-68
Author(s):  
Ludwik Byszewski
Keyword(s):  
Classical Solution ◽  
Differential Inequalities ◽  
Differential Problem ◽  
Nonlinear Parabolic ◽  
Functional Differential

A theorem about a system of strong impulsive degenerate nonlinear parabolic functional-differential inequalities in an arbitrary parabolic set is proved. As a consequence of the theorem, some theorems about impulsive degenerate nonlinear parabolic differential inequalities and the uniqueness of a classical solution of an impulsive degenerate nonlinear parabolic differential problem are established.

scholarly journals Oscillation of the solutions of systems of nonlinear parabolic equations with functional arguments

2007 ◽  
Vol 38 (4) ◽  
pp. 367-379
Author(s):  
Yutaka Shoukaku
Keyword(s):  
Parabolic Equations ◽  
Nonlinear Parabolic Equations ◽  
Differential Inequalities ◽  
Dimensional Problem ◽  
Limit Condition ◽  
Nonlinear Functional ◽  
One Dimensional ◽  
Nonlinear Parabolic ◽  
Functional Differential ◽  
Systems Of Parabolic Equations

In the present paper the oscillatory properties of the solutions of systems of parabolic equations are investigated and oscillation criteria is derived for every solution of boundary value problems to be oscillatory or satisfies some limit condition. Our approach is to reduce the multi-dimensional problem to a one-dimensional problem for nonlinear functional differential inequalities.

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