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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some analogues of Markov and Descartes systems for right disfocality
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by P. W. Eloe and Johnny Henderson
Proc. Amer. Math. Soc. 99 (1987), 543-548
DOI: https://doi.org/10.1090/S0002-9939-1987-0875394-7

Abstract:

A necessary and sufficient condition for the disconjagacy of the $n$th order linear differential equation ${y^{(n)}} + {a_1}(x){y^{(n - 1)}} + \cdots + {a_n}(x)y = 0$ on a compact interval $I$ is that there exists a system of solutions ${y_1}, \ldots ,{y_n}$ such that any one of the following is satisfied: (i) $W({y_1}, \ldots ,{y_k}) > 0,1 \leq k \leq n$, on $I$; (ii) $W({y_i}_{_1}, \ldots ,{y_i}_{_k}) > 0,1 \leq {i_1} < \cdots < {i_k} \leq n,1 \leq k \leq n$, on $I$; or (iii) $W({y_i},{y_{i + 1}}, \ldots ,{y_i}_{ + k - 1}) > 0,1 \leq i \leq n - k + 1,1 \leq k \leq n$, on $I$. Necessary and sufficient criteria for the right disfocality of the linear differential equation on the compact interval $I$ are established in terms of systems of solutions satisfying conditions which are analogous to those given in (i), (ii), (iii).
References
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Bibliographic Information
  • © Copyright 1987 American Mathematical Society
  • 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