Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: TERMINAL VALUE PROBLEM FOR SINGULAR ORDINARY DIFFERENTIAL EQUATIONS: THEORETICAL ANALYSIS AND NUMERICAL SIMULATIONS OF GROUND STATES | TERMINAL VALUE PROBLEM FOR SINGULAR ORDINARY DIFFERENTIAL EQUATIONS THEORETICAL ANALYSIS AND NUMERICAL SIMULATIONS OF GROUND STATES ALEX P PALAMIDES AND THEODOROS G. YANNOPOULOS Received 18 October 2005 Revised 26 July 2006 Accepted 13 August 2006 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. Copyright 2006 A. P. Palamides and T. 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. 1. Introduction In order to study the behavior of nonhomogeneous fluids Dell Isola et al. 6 added an additional term to the volume-free energy E0 p and hence the total energy of the fluid becomes E p l pl2 Eo p 2 Vp 2 Y 0. Then under isothermal process the D Alembert-Lagrange principle can be applied taking into account the conservation of mass on the functional J p u i f p-------E p lVpl2 dtedt t1 Q 2 Hindawi Publishing Corporation Boundary Value Problems Volume 2006 Article ID28719 Pages 1-28 DOI BVP 2006 .
