Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term

This paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on C¹-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ₁(λ) and also show that, the smallest curve μ₁(λ) is positive for all 0 ≤ λ < C_H, with C_H is the optimal constant of Hardy type inequality.