Boundary Value Problems 
Volume 2005 (2005), Issue 3, Pages 307-321
doi:10.1155/BVP.2005.307

The first eigenvalue of p-Laplacian systems with nonlinear boundary conditions

D. A. Kandilakis,1 M. Magiropoulos,2 and N. B. Zographopoulos3

 1Department of Sciences, Technical University of Crete, Chania 73100, Greece
2Science Department, Technological and Educational Institute of Crete, Heraclion 71500, Greece
3Department of Applied Mathematics, University of Crete, Heraklion 71409, Greece
Received 12 October 2004; Revised 21 January 2005

Abstract

We study the properties of the positive principal eigenvalue and the corresponding eigenspaces of two quasilinear elliptic systems under nonlinear boundary conditions. We prove that this eigenvalue is simple, unique up to positive eigenfunctions for both systems, and isolated for one of them.