On the solution sets of differential inclusions and the periodic problem in Banach spaces

✍ Scribed by Ralf Bader; Wojciech Kryszewski

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 476 KB
• Volume: 54
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(03)00098-1

✦ Synopsis

In this paper, the topological structure of the solution set of a constrained semilinear di erential inclusion in a Banach space E is studied. It is shown that the set of all mild solutions, with values in a closed and, in general, thin subset D ⊂ E, is an R -set provided natural boundary conditions and appropriate geometrical assumptions on D (which hold, e.g. when D is convex) are satisÿed. Applications to the periodic problem and to the existence of equilibria are given.