Existence and concentration behavior of ground state solutions for generalized planar quasilinear Schrödinger equations with steep potential well

This work is devoted to the study of ground state solutions for $$ -\text{div}(\text{f}^{2}(u)\nabla u)+\text{f}(u)\text{f}'(u)|\nabla u|^{2}+ \lambda V(x)u=Q(x)g(u),\,\, x\in {\mathbb{R}}^{2}, $$ where $\lambda \geq 1$ , $Q,V: {\mathbb{R}}^{2}\rightarrow {\mathbb{R}}$ and $g: {\mathbb{R}}\rightarrow {\mathbb{R}}$ is Trudinger-Moser type function. Additionally, the concentration behavior of the above ground state is also explored as $\lambda \rightarrow +\infty $ .