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On the principal eigenvalue of degenerate quasilinear elliptic systems. (English) Zbl 1157.35077
Some properties of the principle eigenvalue of a degenerate quasilinear system are studied in the paper. It is proved that this eigenvalue is simple, unique up to positive eigenfunctions and isolated. The regularity of corresponding eigenfunctions is established under certain restrictions on the given data. The extension of the main result to unbounded domains is also discussed.
MSC:
35P30Nonlinear eigenvalue problems for PD operators; nonlinear spectral theory
35J70Degenerate elliptic equations
35J50Systems of elliptic equations, variational methods