Parametrized singular boundary value problems (Q1342351)

Certain \((\varepsilon,\lambda)\)-families of second-order singular ordinary differential equations together with boundary value conditions of the form \(u(0)= u(1)= 0\), \(u(1/2)= a\), \(u(1/5)= b\) are considered. Using some results from his paper [J. Differ. Equations 106, 312-331 (1993)], the author establishes lower estimates for the number of parameters \(\lambda\in \mathbb{R}^ 2\) for which those equations possess a positive solution (\(\varepsilon\geq 0\) small).