Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 06, pp. 16.
Asymptotically periodic solutions for differential and
difference inclusions in Hilbert spaces
Gheorghe Morosanu, Figen Ozpinar
Abstract:
Let
be a real Hilbert space and let
be a
(possibly setvalued) maximal monotone operator. We
investigate the existence of asymptotically periodic solutions to
the differential equation (inclusion)
,
,
where
is a
periodic
function (
)
and
. Consider also the
following difference inclusion (which is a discrete analogue of the
above inclusion):
,
where
,
are
periodic sequences for a positive integer
and
.
We investigate the weak or strong
convergence of its solutions to
periodic sequences. We show that
the previous results due to Baillon, Haraux (1977) and
Djafari Rouhani, Khatibzadeh (2012) corresponding to
,
respectively
,
, remain valid for
, respectively
.
Submitted October 18, 2012. Published January 8, 2013.
Math Subject Classifications: 39A10, 39A11, 47H05, 34G25.
Key Words: Differential inclusion; difference inclusion; subdifferential;
maximal monotone operator; weak convergence; strong convergence.
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Gheorghe Morosanu
Department of Mathematics and its Applications
Central European University
Budapest, Hungary
email: morosanug@ceu.hu


Figen Ozpinar
Bolvadin Vocational School
Afyon Kocatepe University
Afyonkarahisar, Turkey
email: fozpinar@aku.edu.tr

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