Generalization for Amann's and Leggett--Williams' three-solution theorems and applications
Let \(X\) be a nonempty closed convex subset of a real ordered Banach space \(E\) and \(A:X \to X\) a completely continuous operator. The authors give conditions for \(A\) to have at least three fixed points. The results generalize those of \textit{H. Amann} [J. Funct. Anal. 11, 346--384 (1972; Zbl 0244.47046)], \textit{R. W. Leggett} and \textit{L. R. Williams} [Indiana Univ. Math. J. 28, 673--688 (1979; Zbl 0421.47033)], and \textit{R. I. Avery} [Math. Sci. Res. Hot-Line 3, No.~7, 9--14 (1999; Zbl 0965.47038)]. Some applications to two-point boundary value problems are given.
scientific article; zbMATH DE number 2107289