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

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Abstract 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 C 1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ 1(λ) and also show that, the smallest curve μ 1(λ) is positive for all 0 ≤ λ < C H , with C H is the optimal constant of Hardy type inequality.