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T-differentiable functionals and ther critical points

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Abstract

We study critical points of functionalsF: D⊂X→ℝdefined on “nonlinear” setsD in topological vector spacesX. For such functionals, we suggest a notion ofT-derivative and study its connection with other relevant structures. The concept of weak critical point is introduced and the Coleman principle is justified forT-differentiable functionals.

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Authors
  1. V. S. Mel'nik
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Additional information

Institute of Cybernetics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 720–728, June, 1994.

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Mel'nik, V.S. T-differentiable functionals and ther critical points. Ukr Math J 46, 779–789 (1994). https://doi.org/10.1007/BF02658179

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  • DOI: https://doi.org/10.1007/BF02658179

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