J. Gschwindl, I. Rachunkova, S. Stanek, E. Weinmüller:

"Positive blow-up solutions of nonlinear models from real world dynamics";

in: "ASC Report 02/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 24.

In this paper, we investigate the structure and properties of the set of positive blow-up solutions of the differential equation

(tkv′ (t))′ = tk h(t, v(t)), t ∈ (0, T ] ⊂ R,

where k ∈ (1, ∞). The differential equation is studied together with the boundary conditions

lim v(t) = ∞, v(T ) = 0.

t→0+

We specify conditions for the data function h, which guarantee that the set of all positive solutions to the above boundary value problem is nonempty. Further properties of the solutions are

discussed and results of numerical simulations are presented.

Singular ordinary differential equation of the second order, time singularities, blow-up, positive solutions, existence of solutions, polynomial collocation.

http://www.asc.tuwien.ac.at/preprint/2014/asc02x2014.pdf

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