Open Access
november 2013 Periodic forcing for some difference equations in Hilbert spaces
Gheorghe Moroşanu, Figen Özpınar
Bull. Belg. Math. Soc. Simon Stevin 20(5): 821-829 (november 2013). DOI: 10.36045/bbms/1385390766


Let $H$ be a real Hilbert space and let $A:D(A)\subset H\rightarrow H$ be a (possibly multivalued) maximal monotone operator. We are concerned with the difference equation \begin{equation*} \Delta u_{n} + c_{n} A u_{n+1}\ni f_{n},\qquad n=0,1, ... , \end{equation*} where $(c_{n})\subset (0,+\infty)$, $(f_{n})\subset H$ are $p$-periodic sequences for a positive integer $p$. We investigate the existence of periodic solutions to this equation as well as the weak or strong convergence of solutions to $p$-periodic solutions. The first result of this paper (Theorem 1) is a discrete analogue of the 1977 result by Baillon and Haraux (on the periodic forcing problem for the continuous counterpart of the above equation) and was essentially stated by Djafari Rouhani and Khatibzadeh in a recent paper. Here we provide a simpler proof of this result that is based on old existing results due to Browder and Petryshyn and Opial. A strong convergence result is also given and some examples are discussed to illustrate the theoretical results.


Download Citation

Gheorghe Moroşanu. Figen Özpınar. "Periodic forcing for some difference equations in Hilbert spaces." Bull. Belg. Math. Soc. Simon Stevin 20 (5) 821 - 829, november 2013.


Published: november 2013
First available in Project Euclid: 25 November 2013

zbMATH: 1290.39011
MathSciNet: MR3160591
Digital Object Identifier: 10.36045/bbms/1385390766

Primary: 39A10 , 39A11 , 47H05

Keywords: difference equation , maximal monotone operator , partial difference equation , periodic forcing , strong convergence , subdifferential , weak convergence

Rights: Copyright © 2013 The Belgian Mathematical Society

Vol.20 • No. 5 • november 2013
Back to Top