Existence of a principal eigenvalue for the Tricomi problem

Abstract

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 cite{[LP2]} coupled with known results of Krein-Rutman type.

Keywords

• Tricomi problem
• mixed type equations
• spectral theory
• principal eigenvalue
• maximum principle.