Asymptotically periodic solutions to some second-order evolution and difference equations

Abstract

In this paper, we examine the asymptotic periodicity of the solutions of some second-order differential inclusions on associated with maximal monotone operators in a Hilbert space , whose forcing terms are periodic functions perturbed by functions from . It is worth pointing out that strong solutions do not exist in general, so we need to consider weak solutions for this class of evolution inclusions. Similar second-order difference inclusions are also addressed. Our main results on asymptotic periodicity represent significant extensions of the previous theorems proved by R.E. Bruck (1980) and B. Djafari Rouhani (2012).

Keywords:

• periodic solution
• perturbed periodic forcing
• weak asymptotic periodicity

AMS Subject Classifications:

• 47J35
• 34G25
• 47H05
• 47H04

Acknowledgements

The authors are indebted to an anonymous reviewer for some useful comments which led to an improved version of this paper.