Standing waves for quasilinear Schrödinger equations involving double exponential growth

We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation where B₁ denotes the unit ball centered at the origin in R² and g behaves like exp(e^s4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.