In the last years, quasilinear Schrödinger-type equations became a topic of wide interest and they have been derived as a model of several physical phenomena. In this talk, after having recall some classical variational tools, we study the existence of solutions of a generalized version of the quasilinear modified Schrödinger equation in which the coefficient of the principal part depends also on the solution itself.
In particular, the analysis of the interaction of two different norms in a suitable Banach space and a modified version of the Mountain Pass Theorem, allow us to prove the existence of a weak bounded solution.
This is a joint work with Anna Maria Candela and Addolorata Salvatore.