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

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.

Keywords

• Multi-valued differential equation
• Hyper-accretive
• Almost periodicity
• Banach space.