Three symmetric positive solutions for a second-order boundary value problem
The existence of multiple solutions to the second-order boundary value problem \[ y''+ f(y)= 0,\quad 0\leq t\leq 1,\quad y(0)= 0= y(1), \] with \(f: \mathbb{R}\to [0,\infty]\) is analyzed. A supplementary material from the theory of cones in Banach spaces and also a generalization of the Leggett-Williams fixed-point theorem are stated. Growth conditions of \(f\) which allow to apply the generalization of the Legget-Williams fixed-point theorem in obtaining three symmetric positive solutions to the inspecting equations are obtained.
scientific article; zbMATH DE number 1540350
scientific article