We study the existence of solutions to the problem
where or . Extending the works of Wei–Ye and Hyder–Martinazzi to arbitrary odd dimension we show that to a certain extent the asymptotic behavior of and the constant can be prescribed simultaneously. Furthermore if then can be chosen to be any positive number. This is in contrast to the case , , where Jin–Maalaoui–Martinazzi–Xiong showed that necessarily , and to the case , , where C.-S. Lin showed that .
Cite this article
Ali Hyder, Existence of entire solutions to a fractional Liouville equation in . Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 1, pp. 1–14DOI 10.4171/RLM/718