International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 10, Pages 669-677
doi:10.1155/S0161171201003192
On the existence of a solution of a two-point boundary value problem in a cylindrical floating zone
Yongdong Shi1
and Liangsheng Du2
1Research Centre of Financial Engineering, Department of Finance, Dongbei University of Finance and Economics, Box 74, Dalian 116025, China
2Department of Economics, Dongbei University of Finance and Economics, Box 74, Dalian 116025, China
Abstract
Existence of one solution for 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 the problem admits a solution when 0≤Q≤12.683. This improves a recent result where 0≤Q<1.