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Functional Differential Inequalities with Unbounded Delay
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Zdzisław Kamont
Published/Copyright:
March 10, 2010
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.
Key words and phrases:: Maximal solutions; initial problems; unbounded delay; nonlinear estimates of the Perron type; comparison result
Received: 2004-03-07
Published Online: 2010-03-10
Published in Print: 2005-June
© Heldermann Verlag
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Keywords for this article
Maximal solutions;
initial problems;
unbounded delay;
nonlinear estimates of the Perron type;
comparison result
Articles in the same Issue
- Quadric Hypersurfaces Containing a Projectively Normal Curve
- Gelfand Pairs and Generalized d'Alembert's and Cauchy's Functional Equations
- Some Approximation Properties for Modified Baskakov Type Operators
- On a Boundary Value Problem for 𝑛-th Order Linear Functional Differential Systems
- Functional Differential Inequalities with Unbounded Delay
- On Absolutely Negligible Sets in Uncountable Solvable Groups
- Disturbance Due to a Time Harmonic Source in Orthotropic Micropolar Viscoelastic Medium
- Semi-Slant Submanifolds of a Locally Product Manifold
- Boundary Regularity for Capillary Surfaces
- Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces
- Arcwise Connected Continua and Whitney Maps
- On the Fourier Multipliers of the Space 𝐿𝑝
- Some Remarks Concerning Jones Eigenfrequencies and Jones Modes
- On the Strong Differentiation of Multiple Integrals along Different Frames
- On the Asymptotic Behaviour of Solutions of Third Order Delay Differential Equations
- Mapping Properties of Integral Operators of Levy Type
