(untitled) (Balkan Journal of Applied Mathematics and Informatics, 2025)
Variational calculus studied methods for finding maximum and minimum values of functional. It has its inception in 1696 year by Johan Bernoulli with its glorious problem for the brachistochrone: to find a curve, connecting two points A and B , which does not lie in a vertical, so that heavy point descending on this curve from position A to reach position in for at least time. In functional analysis variational calculus takes the same space, as well as theory of maxima and minimum intensity in the classic analysis. In this paper we will prove a theorem for functional where proves that necessary condition for extreme of functional is the variation of functional is equal to zero.