Multiple Solutions for a Class of Hemivariational Inequalities Involving Periodic Energy Functionals
✍ Scribed by D. Goeleven; D. Motreanu; P. D. Panagiotopoulos
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 346 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0170-4214
No coin nor oath required. For personal study only.
✦ Synopsis
In this paper we prove firstly that if f : XP1 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 3X such that o3 j f (u) (here j 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 3X such that u3 j f (u) for some 3 1 , where : XPX* 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.