Existence, multiplicity, and concentration of solutions for generalized quasilinear Schrodinger equations with critical growth

In this paper, we study the following generalized quasilinear Schrodinger equations: -div (epsilon(2)g(2)(u)del u) + epsilon(2)g(u) g'(u) vertical bar del u vertical bar(2) + V(x)u = lambda f (u) + g(u) vertical bar G(u)vertical bar(2*-2)G(u), x is an element of R-N, where epsilon, lambda > 0, N >= 3, g : R -> R+ is a C-1 even function, g(0) = 1 and g'(s) >= 0 for all s >= 0, whereG(u) : = integral(u)(0) g(t) dt. Under some suitable conditions, we study the existence, multiplicity, and concentration of solutions by the variational methods. Published by AIP Publishing.