We study the boundary value problem (Pm, a): f‴ + [(m + 1) / 2] f f″ - m f′ 2 = 0 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.
ASJC Scopus subject areas
- Applied Mathematics