Periodic and Almost Periodic Solutions for Multi-valued Differential Equations in Banach Spaces
Southwest Texas State University, Department of Mathematics
It is known that for ω-periodic differential equations of monotonous type, in uniformly convex Banach spaces, the existence of a bounded solution on ℝ⁺ is equivalent to the existence of an ω-periodic solution (see Haraux  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 ). In this note we want to generalize the results above for multi-valued differential equations.
Multi-valued differential equation, Hyper-accretive, Almost periodicity, Banach space
Hanebaly, E., & Marzouki, B. (2000). Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces. <i>Electronic Journal of Differential Equations, 2000</i>(24), pp. 1-16.