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

We investigate the periodic character of solutions of the
nonlinear difference equation x n + 1 = − 1 / x n + A / x n − 1 . We give sufficient conditions under which every
positive solution of this equation converges to a period two
solution. This confirms a conjecture in the work of DeVault et al.
(2000).

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On the recursive sequence xn+1=−1/xn+A/xn−1

Bounded solutions of some systems of nonlinear functional differential equations with iterated deviating argument

On The Max-Type Equation.

On continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument

The problem of solvability of the following second order system of difference equations zn+1 = αza nw b n, wn+1 = βw c nz d n−1, n ∈N0, where a, b, c, d ∈ Z, α, β ∈ C \ {0}, z−1, z0, w0 ∈ C \ {0}, is studied in detail.

Stevo Stević

Papers

On the recursive sequence xn+1=−1/xn+A/xn−1

Bounded solutions of some systems of nonlinear functional differential equations with iterated deviating argument

On The Max-Type Equation.

On continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument

On a practically solvable product-type system of difference equations of second order