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 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.
Grumiau, C., Squassina, M., Troestler, C., On the mountain pass algorithm for the quasi-linear Schrodinger equation, <<DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B>>, 2013; 18 (5): 1345-1360. [doi:10.3934/dcdsb.2013.18.1345] [http://hdl.handle.net/10807/88876]
On the mountain pass algorithm for the quasi-linear Schrodinger equation
Squassina, MarcoSecondo
;
2013
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 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.
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