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

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 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 < CH, with CH is the optimal constant of Hardy type inequality.

Keywords

• p(·)-biharmonic operator
• variational methods
• ljusternik-schnirelmann theory
• p(·)-hardy’s inequality
• 58e05
• 35j35
• 35j60
• 47j10