An Asymmetric Steklov Problem With Weights: the singular case

Abstract

We prove the existence of a first nonprincipal eigenvalue for an asym-metric Steklov problem with weights. We are interested in the singular case (in where one of the weights has meanvalue zero), this case requires some special attention in connection with the Palais Smale (PS) conditions and with the mountain pass geometry.

Keywords

• Steklov problem
• p-Laplacian
• Asymmetry
• weights
• Nonprincipal eigenvalue
• Cerami (PS) condition.