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For a functional $\E$ and a peak selection that picks up a global maximum of$\E$ on varying cones, we study the convergence up to a subsequence to acritical point of the sequence generated by a mountain pass type algorithm.Moreover, by carefully choosing stepsizes, we establish the convergence of thewhole sequence under a "localization" assumption on the critical point. Weillustrate our results with two problems: an indefinite Schr\"odinger equationand a superlinear Schr\"odinger system.

Convergence of a mountain pass type algorithm for strongly indefinite problems and systems