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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.

MSC:

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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