QUASILINEAR SCHRODINGER EQUATIONS WITH SINGULAR AND VANISHING POTENTIALS INVOLVING NONLINEARITIES WITH CRITICAL EXPONENTIAL GROWTH

In this paper, we study the following class of Schrodinger equations: -Delta(N)u+ V(vertical bar x vertical bar))vertical bar u vertical bar(N-2)u = Q(vertical bar x vertical bar h(u) in R-N, where N >= 2, V, Q: R-N -> R are potentials that can be unbounded, decaying or vanishing at infinity and the nonlinearity h: R -> R has a critical exponential growth concerning the Trudinger Moser inequality. By using a variational approach, a version of the Trudinger Moser inequality and a symmetric criticality type result, we obtain the existence of nonnegative weak and ground state solutions for this class of problems and under suitable assumptions, we obtain a nonexistence result.