On nonlinear perturbations of a periodic elliptic problem in R2 involving critical growth

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Normalized solutions for a Schrödinger equation with critical growth in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{documen (2021, unknown): “We would like to mention that problems involving exponential critical growth have received a special attention at last years, see for example, [4, 5, 7, 8, 14, 18, 19, 20, 21] for semilinear elliptic equations, and [1, 6, 22, 23] for quasilinear equations.”
Existence of a ground state solution for a nonlinear scalar field equation with critical growth (2011, background): “(10) Moreover, we also improve a result in [1] where conditions (9) and (10) have been widely used.”
A nonhomogeneous elliptic problem involving critical growth in dimension two (2008, background): “See also [14] and [4] for related results for homogeneous elliptic problems when the potential V satisfies some geometric condition.”