Variational and Topological Methods: Theory, Applications, 
Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 129-147.

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

Authors: Christopher Grumiau  (Univ. de Mons, Belgium)
         Christophe Troestler (Univ. de Mons, Belgium)
 
Abstract: 
  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 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
  Schrodinger equation  and a superlinear Schrodinger system.


Published February 10, 2014.
Math Subject Classifications: 35J20, 58E05, 58E30, 35B38.
Key Words: Mountain pass algorithm; minimax; steepest descent method;
           Schrodinger equation; spectral gap; strongly indefinite functional; 
           ground state solutions; Nehari manifold; systems.