Copyright © 2009 Zhong Bo Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation: (|f′|p−2f′)′+βrf′+αf+(fq)′=0 satisfying a specific decay rate: lim⁡r→∞rα/βf(r)=0 with α:=(p−1)/(pq−2p+2) and β:=(q−p+1)/(pq−2p+2). Here p>2 and q>p−1. Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection term ut=(|ux|p−2ux)x+(uq)x defined on the half line [0,+∞).