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A Variational Method for Multivalued Operator Equations and some Applications to Mechanics
Author(s) -
Dinca G.
Publication year - 1987
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19871340119
Subject(s) - mathematics , hilbert space , operator (biology) , subderivative , mathematical proof , nonlinear system , mathematical analysis , regular polygon , point (geometry) , convex optimization , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene
A variational method for operator equations of the form Pu + δβ( u ) ∋ f has been given in Dinca [1]. Here P is a (generally) nonlinear operator in a Hilbert space, β: H → − ∞ is a convex, proper (β ≠ + ∞) and lower‐semicontinuous functional and δβ( u ) stands for the subdifferential of β at the point u . The present paper has two parts. The first part contents the main results of Dinca [1] without proofs. The second part discusses particular cases and applications to mechanics among which “the climatisation problem for non‐linear elliptic equations” and its applications.