The authors study the nonlocal boundary value problem \[ -(p(t)y')'+q(t)y=w(t)f(y), \]
\[ \cos \alpha y(a)-\sin \alpha (py')(a)=0,\quad (py')(b)-\int^b_a (py')(s)d\xi(s), \]
where \(a<b\) and the integral is the Riemann-Stieltjes integral with respect to \(\xi(s)\) with \(\xi(s)\) a function of bounded variation. By relating it to the eigenvalues of a linear Sturm-Liouville problem with a two-point separated boundary condition, they obtain results on the existence and nonexistence of nodal solutions of this problem.