On the Mountain-pass algorithm for the quasi-linear Schrodinger equation

TL;DR

This paper explores adapting the Mountain Pass algorithm to solve the quasi-linear Schrödinger equation, addressing challenges posed by nonsmooth functionals where traditional methods fail.

Contribution

It introduces modifications to the Mountain Pass algorithm enabling its application to nonsmooth functionals in quasi-linear Schrödinger equations.

Findings

Successfully applied the adapted algorithm to specific quasi-linear Schrödinger problems.

Demonstrated convergence where classical algorithms are not applicable.

Provided insights into the algorithm's effectiveness for nonsmooth variational problems.

Abstract

We discuss the application of the Mountain Pass algorithm to the so-called quasi-linear Schrodinger equation, which is naturally associated with a class of nonsmooth functionals so that the classical algorithm is not directly applicable.