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Due to the fact that the domain of a variational functional is an infinite-dimensional space, in order to study the extremum problem of functionals, similar to the cases of functions on finite-dimensional spaces, we need to investigate the calculus of variations on infinite-dimensional spaces, especially on Banach spaces, particularly the necessary conditions and sufficient conditions for functional extremum.

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First and Second Order Conditions for Extremum of Functionals

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  • 发表日期：

    2026年

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  • Shiqing Zhang

摘要

Due to the fact that the domain of a variational functional is an infinite-dimensional space, in order to study the extremum problem of functionals, similar to the cases of functions on finite-dimensional spaces, we need to investigate the calculus of variations on infinite-dimensional spaces, especially on Banach spaces, particularly the necessary conditions and sufficient conditions for functional extremum.