A note on a two-point boundary value problem arising from a liquid metal flow

A two-point boundary value problem with a positive parameter Q arising in the study of surface-tension-induced flows of a liquid metal or semiconductor is studied. On the basis of the upper-lower solution method and Schauder's fixed-point theorem, it is proved that when 0 less than or equal to Q less than or equal to 13.213, the problem admits a solution. This improves a recent result where 0 less than or equal to Q less than or equal to 1.