Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

Real and Complex Analysis

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

Generalized composition operators on zygmund spaces and bloch type spaces

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Aufgaben und Lehrsätze aus der Analysis

Closed form formulas for well-defined solutions of a class of difference equations of interest are given. Long term behaviour of well-defined solutions of the equations is presented in detail for the case when the coefficients are constant. We also describe the domain of undefinable solutions of the equation. Our results explain and considerably improve some recent results in the literature.

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On a class of solvable higher-order difference equations

The solvability of a k-dimensional system of difference equations of interest, which extends several recently studied ones, is investigated. A general sufficient condition for the solvability of the system is given, considerably extending some recent results in the literature.

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General k-Dimensional Solvable Systems of Difference Equations

On some linear difference equations and inequalities with continuous argument

Weighted composition operators from the logarithmic weighted-type space to the weighted Bergman space in Cn

Our goal in this paper is to investigate the long-term behavior of solutions of the following difference equation: 𝑥𝑛

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Stevo Stević

Papers

On a class of solvable higher-order difference equations

General k-Dimensional Solvable Systems of Difference Equations

On some linear difference equations and inequalities with continuous argument

Weighted composition operators from the logarithmic weighted-type space to the weighted Bergman space in Cn

Solutions of the Difference Equation ${x}_{n+1}={x}_{n}{x}_{n-1}-1$