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

الملخص EN

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.