Three symmetric positive solutions for a second-order boundary value problem. (English) Zbl 0961.34014

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.


34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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