Qualitative Properties of Solutions for an Integral Equation

Details Qualitative Properties of Solutions for an Integral Equation Qualitative Properties of Solutions for an Integral Equation

2003-07-18

arxiv.org/abs/math/0307262v1

Mathematics

Analysis of PDEs

8 pages

Scientific paper

Let $n$ be a positive integer and let $0 < \alpha < n.$ 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.

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