Contributions to Books:
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,
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/
(u) and for some model problems
from the class of singular differential equations ( (u′))′ + f(t, u′) = g(t, u, u′) discussed in .
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
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.