Existence of Solutions to Nonlinear Schr?dinger Equations Involving N-Laplacian and Potentials Vanishing at Infinity

We study the existence of solutions for the following class of nonlinear Schr?dinger equations-ΔN u+V(x)u=K(x)f(u)in R^N where V and K are bounded and decaying potentials and the nonlinearity f(s)has exponential critical growth.The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.