An uncountable number of solutions for a BVP governing Marangoni convection

This paper investigates a boundary value problem (BVP) governing Marangoni convection over a flat surface. The BVP involves a temperature gradient parameter k>−1k>−1. Previous numerical and analytical studies report the existence of one solution for each value of kk. Here we show that the nature of the solutions varies greatly depending on the value of kk. For each −10k>0.