A note on similarity solutions for boundary layer flows with prescribed heat flux

We study the third-order nonlinear equation: fʹʹʹ + (m + 2)ffʹʹ - (2m + 1)fʹ2 = 0 on (0, (infinity)), subject to the boundary conditions f(0) = (upsilon)(epsilon)R, fʹ((infinity)) = 0 and fʹʹ(0) = -1. The problem arises in the study of similarity solutions for boundary layer flows with prescribed heat flux. We will address the following two open questions which were proposed by Brighi and Hoernel (Math. Methods Appl. Sci. 2005; 28: 479-503): The first one is the uniqueness of bounded solutions for m (epsilon)(-1,-1/2)and (upsilon)>0, and the second one is the structure of solutions for m (epsilon)(-1,-1/2) and (upsilon)>0.