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Monotone Solutions of A Higher Order Neutral Difference Equation
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Sui Sun Cheng
Published/Copyright:
February 23, 2010
Abstract
A real sequence {xk} is said to be (*)-monotone with respect to a sequence {pk} and a positive integer σ if xk > 0 and (–1)nΔn (xk – pkxk–σ) ≥ 0 for n ≥ 0. This paper is concerned with the existence of (*)-monotone solutions of a neutral difference equation. Existence criteria are derived by means of a comparison theorem and by establishing explicit existence criteria for positive and/or bounded solutions of a majorant recurrence relation.
Key words and phrases.: Neutrai difference equation; positive solution; monotone solution; existence theorem
Received: 1995-08-15
Published Online: 2010-02-23
Published in Print: 1998-February
© 1998 Plenum Publishing Corporation
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- Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
- On Three-Dimensional Dynamic Problems of Generalized Thermoelasticity
- Monotone Solutions of A Higher Order Neutral Difference Equation
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Keywords for this article
Neutrai difference equation;
positive solution;
monotone solution;
existence theorem
Articles in the same Issue
- Conditions of the Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for A System of Generalized Ordinary Differential Equations
- On Three-Dimensional Dynamic Problems of Generalized Thermoelasticity
- Monotone Solutions of A Higher Order Neutral Difference Equation
- On the Representation of Numbers by the Direct Sums of Some Binary Quadratic Forms
- Numerical Solutions to the Darboux Problem with the Functional Dependence
- On the Representation of Numbers by Positive Diagonal Quadratic Forms with Five Variables of Level 16
