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G. Pulverer, S. Stanek, E. Weinmüller:
"Analysis and numerical solutions of positive and dead core solutions of singular Sturm-Liouvilee problems";
in: "ASC Report 05/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

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

Singular Sturm-Liouville problem, positive solution, dead core solution, pseudo dead

http://www.asc.tuwien.ac.at/preprint/2009/asc05x2009.pdf