The variational method of Djukic and Vujanovic and its relation to classical variational methods

Abstract

The variational methods are classified into different types according to their Lagrangians, namely, classical-, limit-, adjoint- restricted- and Djukic, Vujanovic (DV)-Lagrangians. For some types, the existence of a Lagrangian to a given equation is discussed and examples are listed. Rules for a general application of the DV-method are presented and the equivalence of the DV-method to other variational methods is shown. This guarantees the identity of the corresponding Euler-Lagrange equations and their (exact) solutions. In special cases, even the approximate variational solutions become identical.