## Differential and Integral Equations

- Differential Integral Equations
- Volume 32, Number 7/8 (2019), 423-454.

### Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature

#### 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.

#### Article information

**Source**

Differential Integral Equations, Volume 32, Number 7/8 (2019), 423-454.

**Dates**

First available in Project Euclid: 2 May 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1556762424

**Mathematical Reviews number (MathSciNet)**

MR3945763

**Subjects**

Primary: 35J30: Higher-order elliptic equations [See also 31A30, 31B30] 53A30: Conformal differential geometry 35R11: Fractional partial differential equations

#### Citation

Hyder, Ali. Structure of conformal metrics on $\mathbb{R}^n$ with constant $Q$-curvature. Differential Integral Equations 32 (2019), no. 7/8, 423--454. https://projecteuclid.org/euclid.die/1556762424