*(English)*Zbl 1181.34025

In this interesting paper, the author studies the nonlocal boundary value problem

where $\alpha [\xb7]$ is a linear functional on $C[0,1]$ given by a Riemann-Stieltjes integral, namely

with $dA$ a *signed* measure. This formulation is quite general and covers classical $m$-point boundary conditions and integral conditions as special cases. The author proves, under suitable growth conditions on the nonlinearity $f$, existence of multiple positive solutions.

Interesting features of this paper are that the theory is illustrated with explicit examples, including a 4-point problem with coefficients with both signs, and that all the constants that appear in the theoretical results are explicitly determined.

The methodology involves classical fixed point index theory and makes extensive use of the results in *J. R. L. Webb* and *G. Infante* [NoDEA, Nonlinear Differ. Equ. Appl. 15, No. 1–2, 45–67 (2008; Zbl 1148.34021)], *J. R. L. Webb* and *K. Q. Lan* [Topol. Methods Nonlinear Anal. 27, 91–115 (2006; Zbl 1146.34020)], *J. R. L. Webb* and *G. Infante* [J. Lond. Math. Soc., II. Ser. 74, No. 3, 673–693 (2006; Zbl 1115.34028)].