On a Schrodinger equation involving fractional (N/s1, q)-Laplacian with critical growth and Trudinger-Moser nonlinearity

A nonlinear Schrodinger equation of fractional (N/s(1), q)-Laplacian is considered with the Rabinowitz potential, critical Sobolev growth and Trudinger-Moser nonlinearity in R-N (-Delta)(N/s1)(s1) u + (-Delta)(q)(s2) u + V(epsilon x)(vertical bar u vertical bar(Ns1-2) u + vertical bar u vertical bar(q-2) u) = lambda f (u) + vertical bar u vertical bar(qs2)*(-2) u. We establish the global existence of nonnegative ground-state solution for suitable parameter values primarily through variational analysis, fractional Trudinger-Moser inequality and mountain pass approach. It is a crucial ingredient to handle three aspects concerning the limiting setting s(1)p = N, the critical Sobolev growth and Trudinger-Moser nonlinearity.