We investigate the existence of soliton solutions of quasilinear
modified Schrödinger equations. Since the classical Laplacian is
replaced by an operator which admits coefficients depending on the
solution itself, a classical variational approach does not work.
Anyaway, by means of approximation arguments on bounded sets and
following some ideas which exploit the interaction between two norms,
the related functional admits a critical point in a “good” Banach space which is a soliton solution of the given problem.
These results are part of joint works with Giuliana Palmieri, Addolorata Salvatore and Caterina Sportelli.
Partial Differential Equations @DipMat 