Classification of Solutions to Conformally Invariant Systems with Mixed Order and Exponentially Increasing or Nonlocal Nonlinearity
Classification of Solutions to Conformally Invariant Systems with Mixed Order and Exponentially Increasing or Nonlocal Nonlinearity
.In this paper, without any assumption on \(v\) and under the extremely mild assumption \(u(x)=O(|x|^{K})\) at \(\infty\) for some \(K\gg 1\) arbitrarily large, we prove classification of solutions to the following conformally invariant system with mixed order and exponentially increasing nonlinearity in \(\mathbb{R}^{2}:\begin {cases} (-\Delta )^{\frac {1}{2}}u(x)=e^{pv(x)}, \qquad x\in \mathbb …