Abstract and Applied Analysis
Volume 7 (2002), Issue 3, Pages 155-167

Quasilinear elliptic systems of resonant type and nonlinear eigenvalue problems

Pablo L. de Nàpoli and M. Cristina Mariani

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.


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=Fv(x,u,v), under conditions involving the first and the second eigenvalues.