Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth

We study the following generalized quasilinear Schrodinger equations with critical growth -div(g(2)(u)del u) + g(u)g'(u)vertical bar del u vertical bar(2) + v(x)u = lambda f(x,u) + g(u)vertical bar G(u)vertical bar(2)*(-2)G(U),x is an element of R-N, where lambda > 0, N >= 3, g(s) : R -> R+ is a C-1 even function, g(0) = 1, and g'(s) >= 0 for all s >= 0, where G (u) = integral(u)(0) g(t)dt Under some suitable conditions, we prove that the equation has a nontrivial solution by variational method.