MULTIPLE SOLUTIONS FOR A CLASS OF HEMIVARIATIONAL INEQUALITIES INVOLVING PERIODIC ENERGY FUNCTIONALS

In this paper we prove firstly that if f:X --> R is a locally Lipschit z function, bounded from below and invariant to a discrete group of di mension N is a suitable sense, acting on a Banach space X, then the pr oblem: find u epsilon X such that o epsilon partial derivative f(u) (h ere partial derivative 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 th e problem: find u epsilon X such that lambda Lambda u epsilon partial derivative f(u) for some lambda epsilon R, where Lambda:X --> X stand s for the duality map. The last two sections are devoted to applicatio ns of the abstract existence results to hemivariational inequalities p ossessing invariance properties. (C) 1997 by B. G. Teubner Stuttgart-J ohn Wiley & Sons Ltd.