On The Multiplicity Of Solutions For Nonhomogeneous Quasilinear Schrodinger Equations

In this paper,we study a class of generalized quasilinear Schrodinger equations of the form-div(g2(u)?u)+g(u)g'(u)|?u|2+?V(x)u= g(u)|G(u)|2*-2G(u)+?h(x),x?RN,where N ?3,??(0,1),s>1,g(t):R ?R+ is a C1 nondecreasing function with respect to |t|,G(t)= ?0t g(?)d?,the potential V(x):RN ?R is positive and h(x)is a nonhomogeneous perturbation term.Under suitable assumptions on ?,V and h,by using Ekeland variational principle and Mountain Pass Lemma,we prove that the problem above has at least two positive solutions.