Some applications of functional-differential inequalities

1987 ◽  
Vol 38 (6) ◽  
pp. 658-661
Author(s):  
D. A. Vzovskii
2005 ◽  
Vol 12 (2) ◽  
pp. 237-254
Author(s):  
Zdzisław Kamont ◽  
Adam Nadolski

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.


Author(s):  
A. D. Myshkis ◽  
D. D. Bainov ◽  
A. I. Zahariev

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.


1995 ◽  
Vol 8 (1) ◽  
pp. 59-68
Author(s):  
Ludwik Byszewski

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.


2007 ◽  
Vol 38 (4) ◽  
pp. 367-379
Author(s):  
Yutaka Shoukaku

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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