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https://doi.org/10.1016/j.aim.2004.07.004
| Title: | Exact solutions of nonlinear conformally invariant integral equations in R3 | Authors: | Xu, X. | Keywords: | Conformally invariant integral equation Exact solution Method of moving spheres |
Issue Date: | 10-Jul-2005 | 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 | URI: | http://scholarbank.nus.edu.sg/handle/10635/103219 | ISSN: | 00018708 | DOI: | 10.1016/j.aim.2004.07.004 |
| Appears in Collections: | Staff Publications |
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