Nonlinear alternatives of Schauder and Krasnosel'skij types with applications to Hammerstein integral equations in \(L^1\) spaces
In this interesting paper, by using the De Blasi measure of weak noncompactness, the authors establish some new variants of nonlinear alternatives of Leray-Schauder and Krasnosel'skij type involving the weak topology of Banach spaces. In addition, the authors apply their abstract results to a nonlinear Hammerstein integral equation in \(L^{1}\) spaces. The main results of this paper complement some recent ones due to \textit{K.\,Latrach, M.\,A.\thinspace Taoudi} and \textit{A.\,Zeghal} [J.~Differential Equations 221, 256--2710 (2006; Zbl 1091.47046)] and \textit{K.\,Latrach} and \textit{M.\,A.\thinspace Taoudi} [Nonlinear Anal.\ 66, 2325--2333 (2007; Zbl 1128.45006)].
scientific article; zbMATH DE number 5804424
scientific article