In this work, we analyze the existence of weak solutions for a singular quasilinear Schrödinger equation in \(\mathbb {R}^2\) involving nonlinearities of double exponential growth. The equation contains two diffusion terms depending on a weight function w(x), which generates a weighted radial Sobolev space allowing us to consider nonlinearities with double exponential growth. More precisely, the nonlinearity g(x, u) behaves like \(\textrm{exp}(e^{|u|^{4\beta }})\) for large |u|, with \(\beta > 1/2\) . The analysis is developed through the dual approach method, which transforms the original problem into a form suitable for variational techniques.
