Variational Problem In this section we consider the limit ! 0 of an abstract minimization problems with a class of functionals containing E . Theorem 3. Let (B; k:k) be a Banach space and let C ` B be nonvoid, convex and weakly closed in B. Let E; F : C ! R [ f1g; be bounded below with inf C E ! 1; inf C F ! 1: We set C := fx 2 C : E(x) ! 1g: For 2 R + let x 2 C. Assume 1. x is for each 2 R + a minimizer of E := E + Gamma1 F in C. 2. x * x 0 weakly in B as ! 0. Then a) lim sup !0 F (x ) inf C F . b) If F is weakly lower sequentially continuous at x 0 , then F (x 0 ) inf C F: c) If F is weakly lower sequentially continuous at x 0 and if E(x 0 ) ! 1, then x 0 is a minimizer of F in C , i.e. F (x 0 ) = inf C F: d) If x is a minimizer of F in C , then lim sup !0 E(x ) E(x ): 14 e) If x is a minimizer of F in C and if E is weakly lower sequentially continuous at x 0 , then E(x 0 ) E(x ): f ) If E and F are we...