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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.

MSC:

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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