Copyright © 2010 Gernot Pulverer et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we investigate the singular Sturm-Liouville problem u′′=λg(u), u′(0)=0, βu′(1)+αu(1)=A, where λ is a nonnegative parameter, β≥0, α>0, and A>0. We discuss the existence of multiple positive solutions and show that for certain values of λ, there also exist solutions that vanish on a subinterval [0,ρ]⊂[0,1), the so-called dead core solutions. The theoretical findings are illustrated by computational experiments for g(u)=1/u and for some model problems from the class of singular differential equations (ϕ(u′))′+f(t,u′)=λg(t,u,u′) discussed in Agarwal et al. (2007). For the numerical simulation, the collocation method implemented in our MATLAB code bvpsuite has been applied.