Multiple positive solutions for a three-point boundary value problem
The author deals with the three-point boundary value problem \[ -x'''+ f(x(t))= 0,\quad x(0)= x'(t_2)= x''(1)= 0\tag{1} \] with \(t_2\in\left[{1\over 2},1\right)\), \(f: \mathbb{R}\to \mathbb{R}\) is continuous and nonnegative for \(x\geq 0\). Using properties of the Green function of the corresponding linear problem and a theorem by \textit{R. W. Leggett} and \textit{L. R. Williams} [Indiana Univ. Math. J. 28, 673-688 (1979; Zbl 0421.47033)], the author proves the existence of at least three positive solutions to (1).
scientific article; zbMATH DE number 1164061