Finding critical points whose polarization is also a critical point

Abstract

We show that near any given minimizing sequence of paths for the mountain pass lemma, there exists a critical point whose polarization is also a critical point. This is motivated by the fact that if any polarization of a critical point is also a critical point and the Euler-Lagrange equation is a second-order semi-linear elliptic problem, T. Bartsch, T. Weth and M. Willem (J. Anal. Math., 2005) have proved that the critical point is axially symmetric.

arXiv comment7 pages

Cited by in corpus (1)

• Local minimizers in spaces of symmetric functions and applications