2019
Том 71
№ 11

$T$-differentiable functionals and ther critical points

Mel'nik V. S.

Abstract

The critical points of the functionals $F:\; D \subset X \rightarrow \mathbb{R}$ defined on "nonlinear" sets $D$ in the topological vector spaces $X$ are studied. A construction of a $T$-derivative is suggested for these functionals and compared with to known constructions. The concept of a weak critical point is introduced and Coleman's principle is justified for $T$-differentiable functionals.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 6, pp 779-789.

Citation Example: Mel'nik V. S. $T$-differentiable functionals and ther critical points // Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 720–728.

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