Some analogues of Markov and Descartes systems for right disfocality

Authors:
P. W. Eloe and Johnny Henderson

Journal:
Proc. Amer. Math. Soc. **99** (1987), 543-548

MSC:
Primary 34B05; Secondary 34B10, 34C10

DOI:
https://doi.org/10.1090/S0002-9939-1987-0875394-7

MathSciNet review:
875394

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Abstract | References | Similar Articles | Additional Information

Abstract: A necessary and sufficient condition for the disconjagacy of the th order linear differential equation on a compact interval is that there exists a system of solutions such that any one of the following is satisfied: (i) , on ; (ii) , on ; or (iii) , on .

Necessary and sufficient criteria for the right disfocality of the linear differential equation on the compact interval are established in terms of systems of solutions satisfying conditions which are analogous to those given in (i), (ii), (iii).

**[1]**E. W. Cheney,*Introduction to approximation theory*, McGraw-Hill, New York, 1966. MR**0222517 (36:5568)****[2]**W. Coppel,*Disconjugacy*, Lecture Notes in Math., vol. 220, Springer-Verlag, New York and Berlin, 1971. MR**0460785 (57:778)****[3]**F. R. Gantmacher,*The theory of matrices*, vol. I, Chelsea, New York, 1960.**[4]**J. S. Muldowney,*A necessary and sufficient condition for disfocality*, Proc. Amer. Math. Soc.**74**(1979), 49-55. MR**521872 (80c:34030)****[5]**-,*On invertibility of linear ordinary differential boundary value problems*, SIAM J. Math. Anal.**12**(1981), 368-384. MR**613318 (82g:34018)****[6]**G. Pólya,*On the mean-value theorem corresponding to a given linear homogeneous differential equation*, Trans. Amer. Math. Soc.**24**(1922), 312-324. MR**1501228**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0875394-7

Keywords:
Disconjugate,
right disfocal,
Markov system,
Descartes system,
Fekete system

Article copyright:
© Copyright 1987
American Mathematical Society