Exact solutions of nonlinear conformally invariant integral equations in R 3
By Xingwang Xu. 2005
52 citations recorded by the source corpus.
Abstract In this paper, we will study the entire positive C 4 solutions of the geometrically interesting integral equation: u ( x ) = 1 8 π ∫ R 3 | x - y | u - q ( y ) dy with 0 q in R 3 . We will show that there are positive entire solutions which take the form u ( x ) = c ( 1 + | x | 2 ) 1 / 2 up to dilation and translations, only when q = 7 .
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/660e29a8fa10341b2ff4ff7491b84fc9d5727316
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In Applied Mathematics
Citations in the corpus
- Nonlinear biharmonic equations with negative exponents (2009, methodology): “Our strategy is to reduce the differential equation to the corresponding integral equation which has been studied by the second author in [26].”
- Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians (2019, methodology): “m 1.10by way ofcontradiction and the method of scaling spheres developed by Dai and Qin [22] (see also [23, 24, 26]). For more related literature on the method of moving planes (spheres), we refer to [2, 3, 4, 6, 7, 8, 9, 10, 12, 14, 17, 18, 19, 21, 25, 27, 30, 31, 32, 34, 39, 40] and the references”
- Sharp reversed Hardy–Littlewood–Sobolev inequality on Rn (2015, methodology): “For interested readers, we refer to [Ser71, GNN79, CGS89, CL91, CLO05, CLO06] for the method of moving planes and its variants, while for the method of moving spheres we refer to [Li04, Xu05].”