Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities

Abstract

Via a constrained minimization, we find a solution $(\hat{I}»,u)$ to the problem \begin{equation*} \begin{cases} (-Δ)^m u+\fracμ{|x|^{2m}}u + λu = ηu^3 + g(u)\\ \int_{\mathbb{R}^{2m}} u^2 \, dx = ρ\end{cases} \end{equation*} with $1\le m\in \mathbb{N}$, $\hat{I}¼,\hat{I}\cdot \ge 0$, $\ddot{I}>0$, and $g$ having exponential critical growth at infinity and mass supercritical growth at zero.

12 pages, online first in Commun. Contemp. Math