Abstract and Applied Analysis
Volume 7 (2002), Issue 5, Pages 287-293
doi:10.1155/S108533750200088X

Isolation and simplicity for the first eigenvalue of the p-Laplacian with a nonlinear boundary condition

Abstract

We prove the simplicity and isolation of the first eigenvalue for the problem Δpu=|u|p−2u in a bounded smooth domain Ω⊂ℝN, with a nonlinear boundary condition given by |∇u|p−2∂u/∂v=λ|u|p−2u on the boundary of the domain.