Existence results for non-coercive variational problems
  The aim of this paper is to give an existence result for a class of one-dimensional, non-convex, non-coercive problems in the Calculus of Variations. The main tools for the proof are an existence theorem in the convex case and the closure of the convex hull of the epigraph of functions strictly convex at infinity. 
Graziano Crasta and Annalisa Malusa