Radial Symmetry and Monotonicity Results for an Integral Equation
نویسندگان
چکیده
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 Rn. 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.
منابع مشابه
Qualitative Properties of Solutions for an Integral Equation
Let n be a positive integer and let 0 < α < n. In this paper, we continue our study of the integral equation u(x) = ∫ R 1 |x− y|n−α u(y)dy. (0.1) 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. AMS Subject Classification 2000 35J99, 45E10, 45G05
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تاریخ انتشار 2004