Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 24, pp. 1-16.
Title: Periodic and almost periodic solutions for multi-valued differential
equations in Banach spaces
Authors: E. Hanebaly (Univ. Mohammed V Faculte des Sciences, Rabat Moroc)
B. Marzouki (Univ. Mohammed V Faculte des Sciences, Rabat Moroc)
Abstract:
It is known that for $\omega$-periodic differential
equations of monotonous type, in uniformly convex Banach spaces,
the existence of a bounded solution on ${\Bbb R}^+$ is equivalent to the
existence of an \omega-periodic solution (see Haraux [5] and
Hanebaly [7, 10]). It is also known that if the Banach space
is strictly convex and the equation is almost periodic and of
monotonous type, then the existence of a continuous solution with
a precompact range is equivalent to the existence of an almost
periodic solution (see Hanebaly [8]).
In this note we want to generalize the results above for multi-valued
differential equations.
Submitted July 16, 1999. Published March 30, 2000.
Math Subject Classifications: 34A60, 34C25, 34C27, 47H10.
Key Words: Multi-valued differential equation; Hyper-accretive;
Almost periodicity; Banach space.