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
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
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.