Solutions for a quasilinear Schrodinger equation: a dual approach

We consider quasilinear stationary Schrodinger equations of the form -Deltau-Delta(u(2))u = g(x,u), x is an element of R-N. (1) Introducing a change of unknown, we transform the search of solutions u(x) of (1) into the search of solutions v(x) of the semilinear equation -Deltav = 1/root1+2f(2)(v) g(x, f (v)), x is an element of R-N, (2) where f is suitably chosen. If v is a classical solution of (2) then u=f(v) is a classical solution of (1). Variational methods are then used to obtain various existence results. (C) 2003 Elsevier Ltd. All rights reserved.