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Multiple Solutions for a Class of Hemivariational Inequalities Involving Periodic Energy Functionals
Author(s) -
Goeleven D.,
Motreanu D.,
Panagiotopoulos P. D.
Publication year - 1997
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/(sici)1099-1476(199704)20:6<547::aid-mma869>3.0.co;2-g
Subject(s) - mathematics , banach space , lipschitz continuity , pure mathematics , hilbert space , invariant (physics) , bounded function , dimension (graph theory) , mathematical analysis , group (periodic table) , combinatorics , mathematical physics , chemistry , organic chemistry
In this paper we prove firstly that if f : X →ℝ is a locally Lipschitz function, bounded from below and invariant to a discrete group of dimension N is a suitable sense, acting on a Banach space X , then the problem: find u ∈ X such that o ∈∂ f ( u ) (here ∂ f ( u ) denotes Clarke's generalized gradient of f at x ) admits at least N +1 orbits of solutions. Then, for a class of discrete groups G of isometries of a Hilbert space X, we establish an existence result for infinitely many G ‐orbits of eigensolutions to the problem: find u ∈ X such that λΛ u ∈∂ f ( u ) for some λ∈ℝ, where Λ: X → X * stands for the duality map. The last two sections are devoted to applications of the abstract existence results to hemivariational inequalities possessing invariance properties. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.