VARIATIONAL PRINCIPLES FOR SUPINF PROBLEMS

For given completely regular topological spaces X and Y and a function f : X x Y -> [-infinity, +infinity] we consider the corresponding supinf problem sup(x is an element of X) inf(y is an element of Y) f(x, y) and provide general conditions under which there exist bounded continuous functions g in X and h in Y with arbitrary small norms such that supinf problem for the perturbed function f + g + h has a solution. The question of well-posedness of the supinf problem is also addressed from this point of view.