Quasilinear elliptic systems of resonant type and nonlinear eigenvalue problems. (English) Zbl 1005.35036

Summary: 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 \(-\Delta_p u = F_{u}(x,u,v)\), \(-\Delta_q v = F_{v} (x,u,v)\), under conditions involving the first and the second eigenvalues.


35J45 Systems of elliptic equations, general (MSC2000)
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J50 Variational methods for elliptic systems
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