On theMountain-Pass algorithm for the quasi-linear Schrödinger equation

Christopher Grumiau; Marco Squassina; Christophe Troestler

doi:10.3934/dcdsb.2013.18.1345

Article Contents

2013, Volume 18, Issue 5: 1345-1360. Doi: 10.3934/dcdsb.2013.18.1345

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On the Mountain-Pass algorithm for the quasi-linear Schrödinger equation

1.
Université de Mons, Institut Complexys, Département de Mathématique, Service d'Analyse Numérique, Place du Parc, 20, B-7000 Mons
2.
Dipartimento di Informatica, Università degli Studi di Verona, Cá Vignal 2, Strada Le Grazie 15, I-37134 Veron

Received: May 2012

Revised: December 2012

Published: July 2013

Abstract / Introduction Related Papers Cited by

Abstract

We discuss the application of the Mountain Pass Algorithm to the so-called quasi-linear Schrödinger 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.

Keywords:

Mathematics Subject Classification: Primary: 35J62, 58E05; Secondary: 35D99, 65N12, 35J70.

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