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
Departamento de Matemática, FCEyN, UBA (1428), Buenos Aires, Argentina
Received 21 May 2001
Copyright © 2002 Sandra Martínez and Julio D. Rossi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.