Boundary Value Problems
Volume 2005 (2005), Issue 3, Pages 307-321
The first eigenvalue of -Laplacian systems with nonlinear boundary conditions
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
Copyright © 2005 D. A. Kandilakis et al. 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.
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.