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

/pdf/aufgaben-und-lehrsatze-aus-der-analysis-mva9fm8nx4.pdf

Aufgaben und Lehrsätze aus der Analysis

Global stability of a difference equation with maximum

This paper finds some lower and upper bounds for the essential norm of the weighted composition operator from -Bloch spaces to the weighted-type space on the unit ball for the case .

/pdf/essential-norms-of-weighted-composition-operators-from-the-g811my77pi.pdf

Essential Norms of Weighted Composition Operators from the -Bloch Space to a Weighted-Type Space on the Unit Ball

Global stability of a max-type difference equation

Solutions of a max-type system of difference equations

This paper studies the boundedness character of positive solutions of the following generalization of a max-type difference equation from automatic control theory (see, Mishkis, (1977) [18] and Popov (1966) [21] ) x n + 1 = max { A , x n p x n − 1 q x n − 2 r } , n ∈ N 0 , where the parameters A , p , q and r are positive numbers. In the study of the equation we also introduce a new method called Oachkatzlschwoif.

Stevo Stević

Papers

Global stability of a difference equation with maximum

Essential Norms of Weighted Composition Operators from the -Bloch Space to a Weighted-Type Space on the Unit Ball

Global stability of a max-type difference equation

Solutions of a max-type system of difference equations

On a generalized max-type difference equation from automatic control theory