QUASILINEAR ELLIPTIC SYSTEMS OF RESONANT TYPE AND NONLINEAR EIGENVALUE PROBLEMS

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 − Δ p u = F u ( x , u , v ), − Δ q v = F v ( x , u , v ), under conditions involving the first and the second eigenvalues.