Open Access

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

Boundary Value Problems20062006:28719

DOI: 10.1155/BVP/2006/28719

Received: 18 October 2005

Accepted: 13 August 2006

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.

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Authors’ Affiliations

(1)
Department of Telecommunications Science and Technology, University of Peloponesse
(2)
Department of Mathematics, Technological Educational Institute (TEI) of Athens

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Copyright

© Palamides and Yannopoulos 2006

This article is published under license to BioMed Central Ltd. 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.