Nodal solutions of boundary value problems with boundary conditions involving Riemann–Stieltjes integrals

We study the nonlinear boundary value problem consisting of the equation −y″=∑i=1mwi(t)fi(y) and a boundary condition involving a Riemann–Stieltjes integral. By relating it to the eigenvalues of the corresponding linear Sturm–Liouville problem with a two-point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. The shooting method and an energy function are used to prove the main results.