Quasilinear Schrödinger equations with bounded coefficients.

We study quasilinear elliptic equations of the form âˆ' div A (u) ∇ u + 1 2 A ′ (u) | ∇ u | 2 + V (x) u = h (u) , u ∈ H 1 ( R N ) , where N â©ľ 3 , A ∈ C 1 (R , R + ) is a bounded function, V (x) is allowed to be singular at the origin, and h ∈ 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. [ABSTRACT FROM AUTHOR]