Elliptic equations in divergence form with zero mass and critical exponential growth

Abstract

In this work, we consider a class of elliptic equations in divergence form with zero mass, involving weight functions that are not necessarily symmetric and nonlinearities satisfying critical exponential growth. For this purpose, we introduce a weighted Trudinger-Moser type inequality. We prove the existence of nonnegative least energy solutions and investigate their qualitative properties, including asymptotic behavior, growth estimates, regularity results, and the existence of strictly positive solutions.