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Asymptotic properties of solutions of difference equation of the form
are studied. Conditions under which every (every bounded) solution of the equation is asymptotically equivalent to some solution of the above equation are obtained. Moreover, the conditions under which every polynomial sequence of degree less than is asymptotically equivalent to some solution of the equation and every solution is asymptotically polynomial are obtained. The consequences of the existence of asymptotically...
Using the method of variation of constants, discrete inequalities and Tychonoff’s fixed-point theorem we study problem asymptotic equivalence of second order difference equations.
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.
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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