Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces

Hanebaly, E. ; Marzouki, B.

Electronic Journal of Differential Equations, Tome 2000 (2000).

Résumé

Summary: 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.

Détail

Classification : 34A60, 34C25, 34C27, 47H10
Keywords: multi-valued differential equation, hyper-accretive, almost periodicity, Banach space