%0 Journal Article
%T Analysis and Numerical Solutions of Positive and Dead Core Solutions of Singular Sturm-Liouville Problems
%A Gernot Pulverer
%A Svatoslav Stan&#283
%A k
%A Ewa B. Weinm&#252
%A ller
%J Advances in Difference Equations
%D 2010
%I Springer
%R 10.1155/2010/969536
%X In this paper, we investigate the singular Sturm-Liouville problem u¡ä¡ä=¦Ëg(u), u¡ä(0)=0, ¦Âu¡ä(1)+¦Áu(1)=A, where ¦Ë is a nonnegative parameter, ¦Â¡Ý0, ¦Á>0, and A>0. We discuss the existence of multiple positive solutions and show that for certain values of ¦Ë, there also exist solutions that vanish on a subinterval [0,¦Ñ] [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 ( (u¡ä))¡ä+f(t,u¡ä)=¦Ëg(t,u,u¡ä) discussed in Agarwal et al. (2007). For the numerical simulation, the collocation method implemented in our MATLAB code bvpsuite has been applied.
%U http://dx.doi.org/10.1155/2010/969536