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)p(x)-growth conditions, where p(x)p(x) is a continuous function defined on the bounded domain with p(x)>1p(x)>1. We prove that the existence of infinitely many eigenvalue sequences and supΛ=+∞supΛ=+∞, where ΛΛ is the set of all eigenvalues. However, unlike the constant case, for a variable exponent p(x)p(x), we present some sufficient conditions for infΛ=0infΛ=0.