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|Title:||Exact solutions of nonlinear conformally invariant integral equations in R3|
|Keywords:||Conformally invariant integral equation|
Method of moving spheres
|Citation:||Xu, X. (2005-07-10). Exact solutions of nonlinear conformally invariant integral equations in R3. Advances in Mathematics 194 (2) : 485-503. ScholarBank@NUS Repository. https://doi.org/10.1016/j.aim.2004.07.004|
|Abstract:||In this paper, we will study the entire positive C4 solutions of the geometrically interesting integral equation: u(x) = 1/8π ∫R3 x-y u-q(y) dy with 0 < q in R3. 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. © 2004 Elsevier Inc. All rights reserved.|
|Source Title:||Advances in Mathematics|
|Appears in Collections:||Staff Publications|
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