Kirchhoff-Schr\"odinger equations in ${\mathbb{R}}^2$ with critical exponential growth and indefinite potential

We obtain the existence of ground state solution for the nonlocal problem $$ m\left(\int_{$\mathbb{R}$^2}(|\nabla u|^2 + b(x)u^2) $\text{d}$x\right)(-\Delta u

• b(x)u) = A(x)f(u) \ \ \ $\text{in}$ \ \ \ $\mathbb{R}$^2, $$where$m$ is a Kirchhoff-type function, $b$ may be negative and noncoercive, $A$ is locally bounded and the function $f$ has critical exponential growth. We also obtain new results for the classical Schr"odinger equation, namely the local case $m\equiv 1$. In the proofs we apply Variational Methods beside a new Trudinger-Moser type inequality.