Existence theorems for inclusions of the type

Abstract

For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chiefly using Ky Fan's fixed point principle. The main result of the paper improves Theorem 1 in [16] as well as Theorem 2.2 of [3]. Some meaningful concrete cases are also presented and discussed.

Keywords:

• operator inclusions in Banach spaces
• Ky Fan's fixed point theorem
• differential equations on the whole space
• mixed usc/Isc conditions

AMS:

• 47H15
• 34A60