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.
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