Abstract
For left — definite singular eigenvalue problems arrising from canonical systems of differential equations a limit-circle criterion is deduced which is at the same time necessary and sufficient. This criterion is applied to differential equations of the form M(η)=λN(η) with M and N differential operators. In case of the Sturm-Liouville-equation the criterion also implies a necessary and sufficient limit-point criterion.
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References
COPPEL, W.A., Stability and Asymptotic Behavior of Differential Equations, Boston: Heath and Company 1965
SCHNEIDER,A. and H.D. NIESSEN, Linksdefinite singuläre kanonische Eigenwertprobleme I. To appear in Journ. f.d. Reine und Angew.Math.
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© 1974 Springer-Verlag
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Niessen, HD. (1974). A necessary and sufficient limit-circle criterion for left-definite eigenvalue problems. In: Sleeman, B.D., Michael, I.M. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065530
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DOI: https://doi.org/10.1007/BFb0065530
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