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(2000 / vol.3 / no.1)
Self-Similar Solutions of a Parabolic Partial Differential Equation
Soyoung Choi, Minkyu Kwak
Pages. 8-11     



In this note we classify positive solutions of an equation
$$Delta u + frac{1}{2} x cdot
abla u + frac{1}{p - 1} u -
|u|^{p - 1} u = 0 , , ,
m{in} , , , f{R}^N,$$ where $1 <
p < (N + 2)/N$. We announce both what is done recently and what
should be done sooner or later.



1. Introduction 2. Behavior near infinity 3. Existence 4. Uniqueness



semilinear elliptic equation, existence and uniqueness, self-similar solution



35J25, 35K15