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Comparison theorems for a right disfocal eigenvalue problem. (English) Zbl 0882.34079

Agarwal, R. P. (ed.), Inequalities and applications. Dedicated to Wolfgang Walter’s 66th birthday with a tribute by R. M. Redheffer. Singapore: World Scientific. World Sci. Ser. Appl. Anal. 3, 149-177 (1994).
Summary: Assuming a certain two term \(n\)th order differential equation is right disfocal we show under certain assumptions the existence of a smallest positive eigenvalue for a related problem. Under further assumptions, we prove the existence of a corresponding eigenfunction in a certain cone. Finally, we prove a comparison theorem for smallest positive eigenvalues for two eigenvalue problems.
For the entire collection see [Zbl 0872.00027].

MSC:

34L05 General spectral theory of ordinary differential operators
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