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

Sandra Martínez and Julio D. Rossi

 Departamento de Matemática, FCEyN, UBA (1428), Buenos Aires, Argentina
Received 21 May 2001

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.