Nodal solutions for a class of degenerate one dimensional BVP's

Abstract

In [Nodal solutions for a class of degenerate boundary value problems, Adv. Nonl. Studies 15 (2015), 253-288], a family of degenerate one dimensional boundary value problems was studied and the existence of positive (and negative) solutions and solutions that possess one interior node was shown for a range of values of a parameter, $\lambda$. It was conjectured that there is a natural extension of these results giving solutions with any prescribed number of interior nodes. This conjecture will be established here.