Geodesic
On the Non-Existence of Conjugate Points
Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 31-37

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we consider the types of pairs of multiple zeros which a solution to the differential equation can possess on an interval I of the real line. The results obtained generalize those in [2] and (for n = 3) in [3].I. Let f satisfy the condition 1.1 for all t ∊ I, u0 ≠ 0, and all u 1, ... u n-1. 
Butler, G. J.; Erbe, L. H.; Mathsen, R. M. On the Non-Existence of Conjugate Points. Canadian mathematical bulletin, Tome 13 (1970) no. 1, pp. 31-37. doi: 10.4153/CMB-1970-006-x
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[1] 1. Bebernes, J. W., A subfunction approach to a boundary value problem for ordinary differential equations, Pacific J. Math. 13, No. 4 (1963), 1053-1066. Google Scholar

[2] 2. Eliason, S. B., Nonperiodicity of solutions of an Nth-order equation, Amer. Math. Monthly (to appear). Google Scholar

[3] 3. Mathsen, R. M., A note on solutions of third-order ordinary differential equations, SIAM Rev. (to appear). Google Scholar

[4] 4. Sherman, T. L., On solutions of Nth-order linear differential equations with N zeros, Bull. Am. Math. Soc. 74, No. 5 (1968), 923-925. Google Scholar

[5] 5. Sherman, T. L., Conjugate points and simple zeros for ordinary linear differential equations (submitted for publication). Google Scholar

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