Quasilinear Schrodinger equations with bounded coefficients

We study quasilinear elliptic equations of the form -div(A(u)del u) + 1/2A'(u)vertical bar del u vertical bar(2) + V(x)u = h(u), u is an element of H-1 (R-N), where N >= 3, A is an element of C-1 (R, R+) is a bounded function, V(x) is allowed to be singular at the origin, and h is an element of C(R, R) is a general nonlinearity. Such type of equations has been derived as models of several physical phenomena corresponding to various types of A. Despite the lack of a priori compactness condition for the energy functional, we develop a new variational approach to deal with the issues of multiple radial solutions, nonradial solutions and sign-changing solutions.