Limit Point Criteria for Differential Equations

Hinton, Don

Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 293-305

Résumé

For certain ordinary differential operators L of order 2n, this paper considers the problem of determining the number of linearly independent solutions of class L2[a, ∞) of the equation L(y) = λy. Of central importance is the operator 0.1 where the coefficients pi are real. For this L, classical results give that the number m of linearly independent L2[a, ∞) solutions of L(y) = λy is the same for all non-real λ, and is at least n [10, Chapter V]. When m = n, the operator L is said to be in the limit-point condition at infinity. We consider here conditions on the coefficients pi of L which imply m = n. These conditions are in the form of limitations on the growth of the coefficients.

Détail

DOI : 10.4153/CJM-1972-024-2

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