Convergence of a mountain pass type algorithm for strongly indefinite problems and systems
Analysis of PDEs
2013-01-09 v1 Numerical Analysis
Abstract
For a functional and a peak selection that picks up a global maximum of on varying cones, we study the convergence up to a subsequence to a critical point of the sequence generated by a mountain pass type algorithm. Moreover, by carefully choosing stepsizes, we establish the convergence of the whole sequence under a "localization" assumption on the critical point. We illustrate our results with two problems: an indefinite Schr\"odinger equation and a superlinear Schr\"odinger system.
Cite
@article{arxiv.1301.1456,
title = {Convergence of a mountain pass type algorithm for strongly indefinite problems and systems},
author = {Christopher Grumiau and Christophe Troestler},
journal= {arXiv preprint arXiv:1301.1456},
year = {2013}
}
Comments
submitted to Proceedings of Electronic Journal of Differential Equations