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On Proper Oscillatory and Vanishing at Infinity Solutions of Differential Equations with A Deviating Argument
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I. Kiguradze
Published/Copyright:
February 23, 2010
Abstract
Sufficient conditions are found for the existence of multiparametrical families of proper oscillatory and vanishing-at-infinity solutions of the differential equation
u(n) (t) = g(t, u(τ0 (t)); . . ., u(m–1) (τm–1(t))),
where n ≥ 4, m is the integer part of 
, g : R+ × Rm → R is a function satisfying the local Carathéodory conditions, and τi : R+ → R (i = 0, . . . , m – 1) are measurable functions such that τ (t) → +∞ for t → + ∞ (i = 0, . . ., m – 1).
Key words and phrases.: Functional differential equation; proper solution; oscillatory solution; vanishing at infinity solution
Received: 1993-12-08
Published Online: 2010-02-23
Published in Print: 1995-August
© 1995 Plenum Publishing Corporation
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Articles in the same Issue
- On Optimal Stopping of Inhomogeneous Standard Markov Processes
- Geometry of Poisson Structures
- Necessary and Sufficient Conditions for Weighted Orlicz Class Inequalities for Maximal Functions and Singular Integrals. I
- On the Solvability of A Spatial Problem of Darboux Type for the Wave Equation
- On Proper Oscillatory and Vanishing at Infinity Solutions of Differential Equations with A Deviating Argument
- Global Dimensions of Subidealizer Rings
- Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras
Keywords for this article
Functional differential equation;
proper solution;
oscillatory solution;
vanishing at infinity solution
Articles in the same Issue
- On Optimal Stopping of Inhomogeneous Standard Markov Processes
- Geometry of Poisson Structures
- Necessary and Sufficient Conditions for Weighted Orlicz Class Inequalities for Maximal Functions and Singular Integrals. I
- On the Solvability of A Spatial Problem of Darboux Type for the Wave Equation
- On Proper Oscillatory and Vanishing at Infinity Solutions of Differential Equations with A Deviating Argument
- Global Dimensions of Subidealizer Rings
- Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras
