Existence criteria for operator inclusions in abstract spaces
The authors obtain existence criteria for the operator equation \(y(t)= Fy(t)\) on \([0,T]\), in a Banach space. The results rely on fixed point theorem of Leray-Schauder type due to Mönch. In addition, the paper presents existence principles for operator inclusions of the form \(y(t)\in Fy(t)\) in Banach spaces. The tool in this case is the nonlinear alternative of Leray-Schauder type for condensing set-valued mappings. Applications are given to Hammerstein integral equations and inclusions.
fixed point theorem of Leray-Schauder type
scientific article; zbMATH DE number 1398403