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

• Main Authors: E. Hanebaly, B. Marzouki
• Format: Article
• Language: English
• Published: Texas State University 2000-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Multi-valued differential equation; Hyper-accretive; Almost periodicity; Banach space.
• Online Access: http://ejde.math.txstate.edu/Volumes/2000/24/abstr.html

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.