Nonlinear Schrödinger equation with unbounded or decaying radial potentials involving exponential critical growth in R2R2

We study the existence and multiplicity of solutions for the following class of nonlinear Schrödinger equations −Δu+V(∣x∣)u=Q(∣x∣)f(u)  inR2, where VV and QQ are unbounded or decaying radial potentials and the nonlinearity f(s)f(s) has exponential critical growth. The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.