Positive solutions of second-order non-local boundary value problem with singularities in space variables (Q481485)

In this interesting manuscript, the author studies the existence of positive solutions of the singular nonlocal boundary value problem \[ \begin{gathered} u''(t)+f(t,u(t),u'(t)) =0,\quad t\in[0,1],\\ au(0)-bu'(0)=\alpha[u],\quad u'(1)=\beta[u], \end{gathered} \] where \(f\) is allowed to be singular, \(a, b>0\) and \(\alpha, \beta\) are linear functionals given by Riemann-Stieltjes integrals, namely \[ \alpha[u]=\int_0^1u(s)dA(s)\quad\text{and}\quad\beta[u]=\int_0^1u(s)dB(s). \] The methodology here is to re-write the problem as a perturbed Hammerstein integral equation and to use the Krasnosel'skiĭ-Guo Theorem on cone compressions and cone expansions.