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Asymptotic properties of solutions of nonautonomous difference equations

Janusz Migda (2010)

Archivum Mathematicum

Asymptotic properties of solutions of difference equation of the form Δ m x n = a n ϕ n ( x σ ( n ) ) + b n are studied. Conditions under which every (every bounded) solution of the equation Δ m y n = b n is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than m is asymptotically equivalent to some solution of the equation and every solution is asymptotically polynomial are obtained. The consequences of the existence of asymptotically...

Asymptotic Solutions of nonlinear difference equations

I. P. van den Berg (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We study the asymptotics of first-order nonlinear difference equations. In particular we present an asymptotic functional equation for potential asymptotic behaviour, and a theorem stating sufficient conditions for the existence of an actual solution with such asymptotic behaviour.

Atomistic to Continuum limits for computational materials science

Xavier Blanc, Claude Le Bris, Pierre-Louis Lions (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The present article is an overview of some mathematical results, which provide elements of rigorous basis for some multiscale computations in materials science. The emphasis is laid upon atomistic to continuum limits for crystalline materials. Various mathematical approaches are addressed. The setting is stationary. The relation to existing techniques used in the engineering literature is investigated.

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