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Existence of a principal eigenvalue for the Tricomi problem. (English) Zbl 1056.35125

Summary: The existence of a principal eigenvalue is established for the Tricomi problem in normal domains; that is, the existence of a positive eigenvalue of minimum modulus with an associated positive eigenfunction. The argument here uses prior results of the authors on the generalized solvability in weighted Sobolev spaces and associated maximum/minimum principles [Commun. Contemp. Math. 2, No. 4, 535–557 (2000; Zbl 1055.35076)] coupled with known results of Krein-Rutman type.

MSC:

35M10 PDEs of mixed type
35P05 General topics in linear spectral theory for PDEs
35B10 Periodic solutions to PDEs

Citations:

Zbl 1055.35076
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