Abstract
Near the end of the eighteenth century, Lagrange observed that a function \(u*\left( x \right)\, \in \,C_0^1\left[ {0\,,\,1} \right]\) which minimizes the functional \(K:\,C_0^1\,\left[ {0,1} \right]\, \to \,R,\) given by
where u′ = du/dx, also makes the bivariate functional δK(u,η) vanish, where
and η is an arbitrary element in \({\text{C}}_{\text{0}}^{\text{1}}\left[ {{\text{0,1}}} \right]\).
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© 1983 Springer-Verlag Berlin Heidelberg
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Oden, J.T., Reddy, J.N. (1983). Mathematical Foundations of Classical Variational Theory. In: Variational Methods in Theoretical Mechanics. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68811-9_2
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DOI: https://doi.org/10.1007/978-3-642-68811-9_2
Publisher Name: Springer, Berlin, Heidelberg
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