Abstract

This paper gives some extended versions of a theorem of \textit{H. Berliocchi} and \textit{J. M. Lasry} in [Bull. Soc. Math. Fr. 101, 129-184 (1973; Zbl 0282.49041)]. It is proved that these versions are equivalent to several extremum principles for classes of mathematical programming problems. An example is given in the last section of the paper to show the ability of using the above results to approach the existence of nonconvex variational and optimal control problems.