Open Access Research Article

Terminal value problem for singular ordinary differential equations: Theoretical analysis and numerical simulations of ground states

Alex P Palamides1* and Theodoros G Yannopoulos2

Author Affiliations

1 Department of Telecommunications Science and Technology, University of Peloponesse, Tripolis 22100, Greece

2 Department of Mathematics, Technological Educational Institute (TEI) of Athens, Egaleo 12210, Greece

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Boundary Value Problems 2006, 2006:28719  doi:10.1155/BVP/2006/28719

Published: 5 November 2006

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.