Eigenvalues for a class of singular problems involving p(x)-Biharmonic operator and q(x)-Hardy potential

In this paper, we consider the nonlinear eigenvalue problem: where is a regular bounded domain of ℝ , ) = , ) the distance function from the boundary , is a positive real number, and functions (⋅), (⋅) are supposed to be continuous on satisfying for any ∈ . We prove the existence of at least one non-decreasing sequence of positive eigenvalues. Moreover, we prove that sup = +∞, where is the spectrum of the problem. Furthermore, we give a proof of positivity of inf > 0 provided that Hardy-Rellich inequality holds.