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Localization properties for nonlinear equations involving monotone operators
Author(s) -
Galewski Marek
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6650
Subject(s) - mathematics , monotone polygon , nonlinear system , hilbert space , banach space , ball (mathematics) , lagrange multiplier , dirichlet distribution , monotonic function , obstacle problem , mathematical analysis , pure mathematics , variational inequality , boundary value problem , mathematical optimization , physics , geometry , quantum mechanics
Using monotonicity methods, the Lagrange multiplier rule, and some variational arguments, we consider a type of localization results pertaining to the existence of critical points to action functionals on a closed ball. A variant of the Schechter critical point theorem on a ball in Hilbert and Banach spaces is obtained. Applications to nonlinear Dirichlet problem and to partial difference equations are given in the final part of this paper.