Multiple symmetric positive solutions for a second order boundary value problem. (English) Zbl 0949.34016

The paper is concerned with the existence of three solutions to the second-order boundary value problem \[ y''+ f(y)=0,\quad 0\leq t\leq 1,\quad y(0)= y(1)= 0,\tag{1} \] where \(f:\mathbb{R}\to [0,\infty)\) is continuous. Under growth conditions imposed on \(f\) the existence of at least three symmetric positive solutions on \((0,1)\) to (1) is proved via the Legett-Williams fixed point theorem. The results are an extension of the earlier ones by Avery, Leggett and Williams, and Guo and Lakshmikantham.


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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