Abstract.
We propose a constructive proof for the Ambrosetti-Rabinowitz Mountain Pass Theorem providing an algorithm, based on a bisection method, for its implementation. The efficiency of our algorithm, particularly suitable for problems in high dimensions, consists in the low number of flow lines to be computed for its convergence; for this reason it improves the one currently used and proposed by Y.S. Choi and P.J. McKenna in [3].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Susanna Terracini: This work is partially supported by M.I.U.R. project “Metodi Variazionali ed Equazioni Differenziali Nonlineari”.
Rights and permissions
About this article
Cite this article
Barutello, V., Terracini, S. A bisection algorithm for the numerical Mountain Pass. Nonlinear differ. equ. appl. 14, 527–539 (2007). https://doi.org/10.1007/s00030-007-4065-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00030-007-4065-9