Abstract
It is shown by means of the classical theory of the transversality conditions of the calculus of variations that certain boundary value problems are equivalent to necessary conditions for the attainment of extreme values of a fundamental integral of a variational problem with variable boundaries. Systems of second order ordinary, as well as partial, differential equations are considered. The method is illustrated for both cases by means of examples, from which well-known theorems of exceptional practical importance emerge effortlessly.
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Rund, H. The reduction of certain boundary value problems to variational problems by means of transversality conditions. Numer. Math. 15, 49–56 (1970). https://doi.org/10.1007/BF02165659
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DOI: https://doi.org/10.1007/BF02165659