Nonstandard variational calculus with applications to classical mechanics. I: An existence criterion
This is Part I of an excellent two part paper that applies Robinson-styled nonstandard analysis to the variational calculus and applications. In this first of two successive parts in the same journal (see also the following review of Part II), the author finds a discretized version of the Euler-Lagrange equation for classical dynamical systems and discusses the existence of an extremum for a given functional in variational calculus. Some results related to the Cauchy existence theorem are obtained and this is coupled with a discussion for various examples.
scientific article; zbMATH DE number 1364373