Geodesic
The Schwarzian Derivative and Disconjugacy of nth order Linear Differential Equations
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 235-249

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

In this paper we deal with the number of zeros of a solution of the nth order linear differential equation 1.1 where the functions pj(z) (j = 0, 1, ..., n – 2) are assumed to be regular in a given domain D of the complex plane. The differential equation (1.1) is called disconjugate in D, if no (non-trivial) solution of (1.1) has more than (n – 1) zeros in D. (The zeros are counted by their multiplicity.)The ideas of this paper are related to those of Nehari (7; 9) on second order differential equations. In (7), he pointed out the following basic relationship. The function 1.2 where y 1(z) and y 2(z) are two linearly independent solutions of 1.3 is univalent in D, if and only if no solution of equation(1.3) has more than one zero in D, i.e., if and only if(1.3) is disconjugate in D. 
Lavie, Meira. The Schwarzian Derivative and Disconjugacy of nth order Linear Differential Equations. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 235-249. doi: 10.4153/CJM-1969-023-9
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