Nonlinear Schrodinger equations involving exponential critical growth with unbounded or vanishing potentials

摘要

In this paper we deal with the following class of nonlinear Schrodinger equations -Delta u + V(vertical bar x vertical bar)u = lambda Q(vertical bar x vertical bar)f(u), x is an element of R-2, where lambda > 0 is a real parameter, the potential V and the weight Q are radial, which can be singular at the origin, unbounded or decaying at infinity and the nonlinearity f(s) behaves like e(alpha s2) at infinity. By performing a variational approach based on a weighted Trudinger-Moser type inequality proved here, we obtain some existence and multiplicity results.