Qualitative Properties of Solutions for an Integral Equation
Abstract
Let
n
be a positive integer and let
0<α<n.
In this paper, we continue our study of the integral equation
u(x) = \int_{R^{n}}
\frac{u(y)^{(n+\alpha)(n-\alpha)}{|x - y|^{n-\alpha}}dy.
We mainly consider singular solutions in subcritical, critical, and super critical cases, and obtain qualitative properties, such as radial symmetry, monotonicity, and upper bounds for the solutions.