Perturbation Theorems for Nash Point Equilibria in the Calculus of Variations

The perturbation problems for Nash point equilibria are studied.By the careful analysis of the singular point set related to a weakly convergent function se-quence.The quasiconvex condition is used to wipe out the obstruction to strong con-vergence or weak lower semi-continuity in proving two perturbation theorems for Nash point equilibria.