Positive solutions of a singular third-order \(m\)-point boundary value problem (Q1951071)

Summary: This paper is concerned with the existence and nonexistence of positive solutions to the singular third-order \(m\)-point boundary value problem \[ \begin{aligned} &u'''(t) + a(t)f(u(t)) = 0,\quad 0 < t < 1,\\ &u(0) = u'(0) = 0,\;u'(1) - \sum^{m-2}_{i=1} \alpha_i u'(\xi_i) = \lambda,\end{aligned} \] where \(\xi_i \in [0, 1)\), \(\alpha_i \in [0, \infty)\) \((i = 1, 2, \dotsc, m - 2)\) are constants, \(\lambda \in (0, 1)\) is a parameter, \(f : [0, \infty) \to [0, \infty)\) is continuous and \(a(\cdot)\) is allowed to be singular at \(t = 0\) and \(t = 1\). The results improve some known results.