This work is devoted to proving existence of nontrivial positivesolutions for a system of n second-order dierential equations subject to integral boundary conditions of Riemann-Stieltjes type and posed on the positive half-line. The novelty of the results is that the nonlinearity involved in the system is sign-changing and depends on the solution and on its derivative. Existence, multiplicity, and nonexistence results of nontrivial positive solutions are obtained using some xed point theorems on suitable cones of a weighted Banach space. A numerical example is included to illustrate the applicability of our results.