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

Weighted iterated radial operators between different weighted Bergman spaces on the unit ball

The solvability of the following system of difference equations $$z_{n+1}=\alpha z_{n}^{a}w_{n}^{b},\qquad w_{n+1}=\beta w_{n-2}^{c}z_{n-2}^{d},\quad n\in {\mathbb {N}}_{0}, $$
 where $a,b,c,d\in {\mathbb {Z}}$
 , $\alpha ,\beta , w_{-2}, w_{-1}, w_{0}, z_{-2}, z_{-1}, z_{0}\in {\mathbb {C}}\setminus\{0\}$
 , is studied in detail by using several methods. The system has the most complex structure of solutions of all the related systems studied so far, and some of the forms of solutions appear for the first time.

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Product-type system of difference equations with a complex structure of solutions

We prove a useful max-type difference inequality which can be applied in studying of some max-type difference equations and give an application of it in a recent problem from the research area. We also give a representation of solutions of the difference equation 𝑥𝑛=max{𝑥𝑎1𝑛−1,…,𝑥𝑎𝑘𝑛−𝑘}.

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On a Max-Type Difference Inequality and Its Applications

Asymptotically convergent solutions of a system of nonlinear functional differential equations of neutral type with iterated deviating arguments

We prove an inclusion theorem regarding a system of difference equations and apply it in getting the asymptotics of some solutions of some concrete difference equations.

Stevo Stević

Papers

Weighted iterated radial operators between different weighted Bergman spaces on the unit ball

Product-type system of difference equations with a complex structure of solutions

On a Max-Type Difference Inequality and Its Applications

Asymptotically convergent solutions of a system of nonlinear functional differential equations of neutral type with iterated deviating arguments

On the asymptotics of some systems of difference equations