摘要
We study the boundary value problem (P <sub>m, a</sub> ): f <sup>‴</sup> + [(m + 1) / 2] f f <sup>″</sup> - m f <sup>′ 2</sup> = 0 on (0, + ∞), subject to the boundary conditions f (0) = a ∈ R, f <sup>′</sup> (0) = - 1 and f <sup>′</sup> (+ ∞) = 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 (P <sub>m, a</sub> ) for the physical interesting case: m < - 1 and a ≥ 0. © 2009 Elsevier Inc. All rights reserved.