Some Boundary Value Problems for Generalized Differential Equations

Abstract

Two versions of the Ważewski retract method are proven for generalized differential equations. These theorems are then applied to study some two-point boundary value problems for second order generalized differential equations of the type $x'' \in G( {t,x,x'} )$, where $G( {t,x,x'} )$ is an upper semicontinuous, compact, convex set-valued mapping.