On the spectrum of a fourth order elliptic equation with variable exponent

We study the eigenvalues for a fourth order elliptic equation with p(x)-growth conditions, where p(x) is a continuous function defined on the bounded domain with p(x) > 1. We prove that the existence of infinitely many eigenvalue sequences and sup Lambda = +infinity. where Lambda is the set of all eigenvalues. However, unlike the constant case, for a variable exponent p(x), we present some sufficient conditions for inf Lambda = 0. Crown Copyright (C) 2009 Published by Elsevier Ltd. All rights reserved.