Solutions for a quasilinear Schrödinger equation: a dual approach Original Research Article

We consider quasilinear stationary Schrödinger equations of the form equation(1) View the MathML source 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 equation(2) View the MathML source 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.