Existence and Uniqueness of Very Singular Solution of a Degenerate Parabolic Equation with Nonlinear Convection

We here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation: [inline-graphic not available: see fulltext] satisfying a specific decay rate: [inline-graphic not available: see fulltext] with [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext]. Here [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext]. Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection term [inline-graphic not available: see fulltext] defined on the half line [inline-graphic not available: see fulltext].