Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 32, pp. 1-11.

Title: Discussion of a uniqueness result in ``Equilibrium Configurations for a Floating Drop''
       
Author: Raymond Treinen (Texas State Univ. TX, USA)

Abstract: 
We analyze a uniqueness result presented by Elcrat, Neel, and Siegel [1]
for unbounded liquid bridges, and show that the proof they presented is incorrect.
We add a hypothesis to their stated theorem and prove that their result holds under
this condition.  Then we use Chebyshev spectral methods to approximate solutions
to certain boundary value problems used to check this hypothesis holds at least on
a range of cases.

Submitted July 22, 2022. Published April 03, 2023.
Math Subject Classifications: 35Q35, 76A02.
Key Words: Capillarity; unbounded liquid bridges; uniqueness.