On a Relation Between a Theorem of Hartman and a Theorem of Sherman
Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 275-281

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We are concerned with the nth-order linear differential equation 1 where the coefficients are assumed to be continuous. Hartman [1] proved that (see Definition 2) the first conjugate point η1 (t) of t satisfies 2 Hartman actually proved a more general result which has very important applications in nonlinear differential equations.
Peterson, A. C. On a Relation Between a Theorem of Hartman and a Theorem of Sherman. Canadian mathematical bulletin, Tome 16 (1973) no. 2, pp. 275-281. doi: 10.4153/CMB-1973-046-7
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[1] 1. Hartman, P., Unrestricted n-parameter families, Rend. Circ. Mat. Palermo (2) 7 (1958), 123–142. Google Scholar

[2] 2. Opial, Z., On a theorem of O. Arama, J. Differential Equations 3 (1967), 88–91. Google Scholar

[3] 3. Sherman, T. L., Conjugate points and simple zeros for ordinary differential equations, Trans. Amer. Math. Soc. 146 (1969), 397–411. Google Scholar

[4] 4. Kim, W. J., Simple zeros of solutions of nth-order linear differential equations, Proc. Amer. Math. Soc. (2) 28 (1971), 557–561. Google Scholar

[5] 5. Sherman, T. L., Properties of solutions of nth order linear differential equations, Pacific J. Math. 15 (1965), 1045–1060. Google Scholar

[6] 6. Peterson, A. C., On the ordering of multi-point boundary value functions, Canad. Math. Bull. (4) 13 (1970), 507–513. Google Scholar

[7] 7. Peterson, A. C., Distribution of zeros of solutions of a fourth order differential equation, Pacific J. Math. 30 (1969), 751–764. Google Scholar

[8] 8. Polya, G., On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1922), 312–324. Google Scholar

[9] 9. Nehari, Z., Disconjugate linear differential operators, Trans. Amer. Math. Soc. 129 (1967), 500–516. Google Scholar

[10] 10. Peterson, A. C., The distribution of zeros of extremal solutions of a fourth order differential equation for the nth conjugate point, J. Differential Equations 8 (1970), 502–511. Google Scholar

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