Some remarks on an eigenvalue problem for an anisotropic elliptic equation with indefinite weight

Abstract

In this paper, we consider an eigenvalue problem for an anisotropic elliptic equation with indefinite weight, in which the differential operator involves partial derivatives with different variable exponents. Under some suitable conditions on the growth rates of the anisotropic coefficients involved in the problem, we prove some results on the existence and non-existence of a continuous family of eigenvalues by using variational methods.