ON THE MOUNTAIN-PASS ALGORITHM FOR THE QUASI-LINEAR SCHRÖDINGER EQUATION

摘要

We discuss the application of the Mountain Pass Algorithm to the so-called quasi-linear Schroedinger equation, which is naturally associated with a class of nonsmooth functionals so that the classical algorithm cannot directly be used. A change of variable allows us to deal with the lack of regularity. We establish the convergence of a mountain pass algorithm in this setting. Some numerical experiments are also performed and lead to some conjectures.