Advances in Difference Equations
Volume 2010 (2010), Article ID 969536, 37 pages
Research Article

Analysis and Numerical Solutions of Positive and Dead Core Solutions of Singular Sturm-Liouville Problems

1Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 6-10, 1040 Vienna, Austria
2Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic

Received 20 December 2009; Accepted 28 April 2010

Academic Editor: Josef Diblik

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.


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, β0, 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.