A new variational principle

A variational principle, an extension of the principle of Ekeland, is derived by nonstandard means. Its domain of application is wider than the original principle, and can be applied to functions which are lower semicontinuous on finite-dimensional subspaces of a linear space. An example is given, in which the principle is applied, first, to a nonclassical variational problem, consisting of the minimization of an integral functional with a discontinuous integrand, and then to the derivation of a general Principle of the Maximum, with integral performance criterion with, also, a discontinuous integrand. A brief Appendix is included, giving the main concepts and construction of nonstandard analysis as needed in the text.