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

Abstract

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 l _p -multipliers. We also give results on boundedness and asymptotic behaviour for semilinear discrete evolution equations.

Keywords:

• well-posedness
• discrete time
• second order evolution equations
• perturbation theory
• stability
• boundedness

2000 Mathematics Subject Classification::

• 39A12
• 39A11
• 47D06

Notes

1. [email protected]

2. This author is partially supported by CNPQ/Brazil under Grant 300365/2008-0.

Additional information

Notes on contributors

Airton Castro

1

Claudio Cuevas

2