Abstract
In this article, we study the nonlocal equation $$ (-\Delta)^{\frac{n}{2}}u=(n-1)!e^{nu}\quad \text{in $\mathbb R$}, \quad\int_{\mathbb R}e^{nu}dx < \infty, $$ which arises in the conformal geometry. Inspired by the previous work of C.S. Lin and L. Martinazzi in even dimension and T. Jin, A. Maalaoui, L. Martinazzi, J. Xiong in dimension three, we classify all solutions to the above equation in terms of their behavior at infinity.
Citation
Ali Hyder. "Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature." Differential Integral Equations 32 (7/8) 423 - 454, July/August 2019. https://doi.org/10.57262/die/1556762424