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]. © 2007 Birkhaueser.
Barutello, V., Terracini, S. (2007). A bisection algorithm for the numerical mountain pass. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 14(5-6), 527-539 [10.1007/s00030-007-4065-9].
A bisection algorithm for the numerical mountain pass
TERRACINI, SUSANNA
2007
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]. © 2007 Birkhaueser.
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