On the spectrum of a fourth order nonlinear eigenvalue problem with variable exponent and indefinite potential

The present paper deals with the spectrum of a fourth order nonlinear eigenvalue problem involving variable exponent conditions and a sign-changing potential. The main result of this paper establishes the existence of two positive constants lambda(0) and lambda(1) with lambda(0) <= lambda(1) such that every lambda is an element of [lambda(1), +infinity) is an eigenvalue, while lambda is an element of (-infinity, lambda(0)) cannot be an eigenvalue of the above problem.