Generalizations of Krasnosel'skiĭ's fixed point theorem in cones and applications (Q519486)

The author proves several fixed point results for completely continuous maps on cones in Banach spaces in the spirit of \textit{R. W. Leggett} and \textit{L. R. Williams} [Indiana Univ. Math. J. 28, 673--688 (1979; Zbl 0421.47033)] \{the page numbers for this item are missing in the bibliography\}. The details are (to put it mildly) somewhat technical. In addition, the author proves the existence of a positive solution to the boundary problem \(u''(t)+f(t,u(t))=0\) on \([0,1]\) with zero boundary conditions with a non-negative continuous right hand side \(f:[0,1]\times\mathbb{R}_+\to\mathbb{R}_+\).