Abstract
This project addresses the study of a class of elliptic problems. The investigation focuses on finding solutions to partial differential equations (PDEs) of the form Lu(x) + V(x)u = f(x, u), ýx ©, in a domain © R^n, and some of their properties. Here, Lu(x) is a general elliptic operator, V(x) is a potential, and f(x, u) represents the nonlinearity with critical exponential growth. The…