Similarity solutions for liquid metal systems near a sharply cornered conductive region

We study the boundary value problem (Pm,a): on (0,+∞), subject to the boundary conditions f(0)=a∈R, f′(0)=−1 and f′(+∞)=0. The problem arises in the study of similarity solutions for high frequency excitation of liquid metal systems in an antisymmetric magnetic field. We give a complete picture of solutions of (Pm,a) for the physical interesting case: m<−1 and a⩾0.