Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-15T18:41:36.587Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Relation Between a Theorem of Hartman and a Theorem of Sherman

Published online by Cambridge University Press:  20 November 2018

A. C. Peterson
A. C. Peterson*
Affiliation:
University of Nebraska, Lincoln, Nebraska
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 275 - 281
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Hartman, P., Unrestricted n-parameter families, Rend. Circ. Mat. Palermo (2) 7 (1958), 123–142.Google Scholar
2. Opial, Z., On a theorem of O. Arama, J. Differential Equations 3 (1967), 88–91.Google Scholar
3. Sherman, T. L., Conjugate points and simple zeros for ordinary differential equations, Trans. Amer. Math. Soc. 146 (1969), 397–411.Google Scholar
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. Sherman, T. L., Properties of solutions of nth order linear differential equations, Pacific J. Math. 15 (1965), 1045–1060.Google Scholar
6. Peterson, A. C., On the ordering of multi-point boundary value functions, Canad. Math. Bull. (4) 13 (1970), 507–513.Google Scholar
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. 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. Nehari, Z., Disconjugate linear differential operators, Trans. Amer. Math. Soc. 129 (1967), 500–516.Google Scholar
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