Existence of Kelvin-Invariant Positive Solutions for Critical Elliptic Equations with Variable Coefficients via Profile Decomposition

Yohei Sato, Reo Suzuki

In this paper, we consider the following critical nonlinear elliptic equation: \[ - Δu = a(x) |u|^{2^*-2}u \quad \text{in } \mathbb{R}^N, \quad u \in \mathcal{D}^{1,2}(\mathbb{R}^N…