New Developments in Difference Equations and Applications

Proceedings of the Third International Conference on Difference Equations

SuiSun Cheng, Sui Sun Cheng, Saber N. Elaydi

• Publisher: Routledge
• Year: 2017
• eBook ISBN: 9781351428804
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

The late Professor Ming-Po Chen was instrumental in making the Third International Conference on Difference Equations a great success. Dedicated to his memory, these proceedings feature papers presented by many of the most prominent mathematicians in the field. It is a comprehensive collection of the latest developments in topics including stability theory, combinatorics, asymptotics, partial difference equations, as well as applications to biological, social, and natural sciences. This volume is an indispensable reference for academic and applied mathematicians, theoretical physicists, systems engineers, and computer and information scientists.

ON THE NONAUTONOMOUS EQUATION $x_{n+1}=\max \left\{\frac{A_n}{x_n},\frac{B_n}{x_{n-1}}\right\}$

W.J. BRIDEN, E.A. GROVE,
G. LADAS and L.C. MCGRATH

Department of Mathematics
University of Rhode Island
Kingston, RI 02881, U.S.A.

Abstract We study the boundedness and the periodic character of the solutions of the nonautonomous equation

$x_{n+1}=\text{max}\left\{\frac{A_n}{x_n},\frac{B_n}{x_{n-1}}\right\},n=0,1,\dots$

where ${\left\{A_n\right\}}_{n=0}^{\infty }$ and ${\left\{B_n\right\}}_{n=0}^{\infty }$ are sequences of negative real numbers, and where the initial conditions x_–1 and ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• List of Contributors
• List of Registered Participants
• BOUNDEDNESS OF SOLUTIONS OF A PLANT-HERBIVORE SYSTEM
• CONNECTION MATRICES AND RIEMANN-HILBERT PROBLEM FOR q-DIFFERENCE EQUATIONS
• A MATHEMATICAL MODEL OF A DISCRETE NONLINEAR OSCILLATOR
• THE ROLE OF INVARIANCE IN THE THEORY OF NON-AUTONOMOUS DIFFERENCE EQUATIONS
• A METHOD FOR SOLVING SECOND ORDER DIFFERENCE EQUATIONS
• ON THE NON-AUTONOMOUS EQUATION xn+1 = max{An/xn, Bn/xn-1}
• ON SYSTEMS OF VOLTERRA DIFFERENCE EQUATIONS ASSOCIATED WITH COLLOCATION METHODS FOR WEAKLY SINGULAR VOLTERRA INTEGRAL EQUATIONS
• STABILITY OF PARTIAL DIFFERENCE EQUATIONS
• CONTINUATION-CONJUGATE GRADIENT ALGORITHMS FOR SEMILINEAR ELLIPTIC NEUMANN PROBLEMS
• RECENT DEVELOPMENTS IN THE ASYMPTOTICS OF DIFFERENCE EQUATIONS
• EXISTENCE AND UNIQUENESS OF BOUNDED SOLUTIONS FOR A CLASS OF DIFFERENCE SYSTEMS WITH DICHOTOMIES OF SUMMABLE TYPE
• FINDING INVARIANT REGIONS OF NON-AUTONOMOUS LYNESS-TYPE DIFFERENCE EQUATIONS
• ON A DISCRETE MODEL OF MUTUALISM
• PARTIAL DIFFERENCE EQUATIONS: CAUCHY PROBLEM AND FUNDAMENTAL SOLUTIONS
• ASYMPTOTIC CONSTANCY TO THE NEUTRAL DELAY DIFFERENCE EQUATION
• ASYMPTOTIC BEHAVIOURS OF VOLTERRA DIFFERENCE EQUATIONS
• ON THE RECURSIVE SEQUENCE xn+1 = max{A/xpn, 1/xqx-1}
• EXPLICIT NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATIONS OF TWO DIFFERENCE EQUATIONS
• SYMMETRY FORMATION IN THE DISCRETE HEAT EQUATION
• ON THE BEHAVIOR OF A RATIONAL FIRST ORDER EQUATION
• SOME SPECTRAL PROPERTIES OF THE SOLUTION OPERATOR FOR LINEAR VOLTERRA DIFFERENCE SYSTEMS
• DISCRETE KURAMOCHI FUNCTION
• ASYMPTOTIC BEHAVIOR OF A SYSTEM OF HIGHER ORDER LINEAR RECURRENCE EQUATIONS
• FINITE DIFFERENCE EQUATIONS AND PERIODICITY
• ESTIMATE OF STABILITY REGION FOR DELAY DIFFERENCE EQUATIONS