Radial Symmetry and Monotonicity Results for an Integral Equation

Details Radial Symmetry and Monotonicity Results for an Integral Equation Radial Symmetry and Monotonicity Results for an Integral Equation

2004-10-12

arxiv.org/abs/math/0410287v1

Mathematics

Analysis of PDEs

8 pages

Scientific paper

In this paper, we consider radial symmetry property of positive solutions of an integral equation arising from some higher order semi-linear elliptic equations on the whole space $\mathbf{R}^n$. We do not use the usual way to get symmetric result by using moving plane method. The nice thing in our argument is that we only need a Hardy-Littlewood-Sobolev type inequality. Our main result is Theorem 1 below.

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