Abstract and Applied Analysis
Volume 7 (2002), Issue 3, Pages 155-167
doi:10.1155/S1085337502000829
Quasilinear elliptic systems of resonant type and nonlinear eigenvalue problems
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires (1428), Argentina
Received 20 February 2001
Copyright © 2002 Pablo L. de Nàpoli and M. Cristina Mariani. 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
This work is devoted to the study of a quasilinear elliptic
system of resonant type. We prove the existence of infinitely
many solutions of a related nonlinear eigenvalue problem.
Applying an abstract minimax theorem, we obtain a solution of the
quasilinear system −Δpu=Fu(x, u, v), −Δqv=F v(x, u, v), under conditions involving the first and the second eigenvalues.