title: Convergence of Toland's critical points for sequences of DC functions and application to the resolution of semilinear elliptic problems
abstract: We prove that if a sequence (f/sub n/)/sub n/ of DC functions (difference of two convex functions) converges to a DC function f in some appropriate way and if u/sub n/ is a critical point of f/sub n/, in the sense described by Toland (1978, 1979), and is such that (u/sub n/)/sub n/ converges to u, then u is a critical point of f, still in Toland's sense. We also build a new algorithm which searches for this critical point u and then apply it in order to compute the solution of a semilinear elliptic equation
keyphrases: semilinear elliptic problems semilinear elliptic equation critical point convergence DC function sequences convex function difference