Qualitative Properties of Solutions for an Integral Equation

Chen, Wenxiong; Li, Congming; Ou, Biao

Qualitative Properties of Solutions for an Integral Equation

Authors

Chen, Wenxiong

Li, Congming

Ou, Biao

Description

Let $n$ be a positive integer and let $0 < α< n.$ In this paper, we continue our study of the integral equation $$ u(x) = \int_{R^{n}} \frac{u(y)^{(n+α)(n-α)}{|x - y|^{n-α}}dy.$$ 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.
8 pages