Abstract and Applied Analysis
Volume 2012 (2012), Article ID 582746, 21 pages
http://dx.doi.org/10.1155/2012/582746
Research Article

Existence and Stability of the Solution of a Nonlinear Boundary Value Problem

Agneta M. Balint1 and Stefan Balint2

1Faculty of Physics, West University of Timisoara, Bulevard V.Parvan 4, 300223 Timisoara, Romania
2Faculty of Mathematics and Computer Science, West University of Timisoara, Bulevard V.Parvan 4, 300223 Timisoara, Romania

Received 31 July 2012; Accepted 5 November 2012

Academic Editor: Carlos Lizama

Copyright © 2012 Agneta M. Balint and Stefan Balint. 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

The purpose is to find conditions assuring the existence of solutions for a nonlinear, boundary value problem in case of the axis-symmetric Young-Laplace differential equation. The equation describes the capillary surface between two static fluids. Necessary or sufficient conditions are found for the existence of a solution. The static stability of the obtained solution is also analyzed and stability or instability results are revealed. For the NdYAG microfiber growth, by the pulling-down method, numerical illustrations are given.