Perturbation theory, stability, boundedness and asymptotic behaviour for second order evolution equation in discrete time.

This work deals with the existence, uniqueness and stability of solutions for semilinear discrete second order evolution equations in Banach spaces by using recent characterization of well-posedness for second order evolution equations in terms of R-boundedness and lp-multipliers. We also give results on boundedness and asymptotic behaviour for semilinear discrete evolution equations. [ABSTRACT FROM AUTHOR]