TITLE:
An Estimate on Linear Functionals’ Kernels in Banach Spaces, and Regularity of Convex Functionals
AUTHORS:
Hiroko Okochi
KEYWORDS:
Banach Space, Convex Functional, Subdifferential, Frèchet Derivative, Gâteaux Derivative, Deformation Lemma, Mountain Pass Theorem
JOURNAL NAME:
Applied Mathematics,
Vol.13 No.9,
September
19,
2022
ABSTRACT: Motivated to obtain the second critical point of a nonlinear differential equation, which is expressed by derivatives of convex functional defined on a Banach space, an estimate withis given to see the relation between f-1(0) and g-1(0). And both the Fréchet differentiability and the continuity of Fréchet derivative of every convex functional defined on an open subset of a Banach space are shown.