Boundary Value Problems
Volume 2006 (2006), Article ID 28719, 28 pages
doi:10.1155/BVP/2006/28719
Terminal value problem for singular ordinary differential equations: Theoretical analysis and numerical simulations of ground states
1Department of Telecommunications Science and Technology, University of Peloponesse, Tripolis 22100, Greece
2Department of Mathematics, Technological Educational Institute (TEI) of Athens, Egaleo 12210, Greece
Received 18 October 2005; Revised 26 July 2006; Accepted 13 August 2006
Copyright © 2006 Alex P. Palamides and Theodoros G. Yannopoulos. 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.
Abstract
A singular boundary value problem (BVP) for a second-order
nonlinear differential equation is studied. This BVP is a model in
hydrodynamics as well as in nonlinear field theory and especially in the
study of the symmetric bubble-type solutions (shell-like theory). The
obtained solutions (ground states) can describe the relationship between
surface tension, the surface mass density, and the radius of the spherical
interfaces between the fluid phases of the same substance. An interval of
the parameter, in which there is a strictly increasing and positive
solution defined on the half-line, with certain asymptotic behavior is
derived. Some numerical results are given to illustrate and verify our
results. Furthermore, a full investigation for all other types of solutions
is exhibited. The approach is based on the continuum property
(connectedness and compactness) of the solutions funnel (Knesser's theorem),
combined with the corresponding vector field's ones.