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 composition operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball

A note on polyharmonic functions

In this paper, we present an isometric extension from the unit sphere of a subspace of s p ( α ) to the whole space s p ( α ) . We obtain that the Lamperti isometric mapping of the unit sphere S ( s p ( α ) ) into itself can be extended to an isometry on the whole space s p ( α ) .

The problem of isometric extension in the unit sphere of the space sp(α)

On bounded continuously differentiable solutions with Lipschitz first derivatives of a system of functional differential equations

Abstract We study a nonlinear second-order difference equation which considerably extends some equations in the literature. Our main result shows that the difference equation is solvable in closed form. Some applications of the main result are also given. 

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Stevo Stević

Papers

Weighted iterated radial composition operators from logarithmic Bloch spaces to weighted-type spaces on the unit ball

A note on polyharmonic functions

The problem of isometric extension in the unit sphere of the space sp(α)

On bounded continuously differentiable solutions with Lipschitz first derivatives of a system of functional differential equations

On a nonlinear second-order difference equation