Nodal solutions of nonlocal boundary value problems

Abstract

We study the nonlinear boundary value problem consisting of the second order differential equation on [a, b] and a boundary condition involving a Riemann‐Stieltjes integral. By relating it to the eigenvalues of a 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. We also discuss the changes of the existence of different types of nodal solutions as the problem changes.

First published online: 14 Oct 2010