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

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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Correspondence to Alex P Palamides.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Palamides, A.P., Yannopoulos, T.G. Terminal value problem for singular ordinary differential equations: Theoretical analysis and numerical simulations of ground states. Bound Value Probl 2006, 28719 (2006). https://doi.org/10.1155/BVP/2006/28719

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  • DOI: https://doi.org/10.1155/BVP/2006/28719

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