A sufficient condition for eventual disconjugacy
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- by William F. Trench
- Proc. Amer. Math. Soc. 52 (1975), 139-146
- DOI: https://doi.org/10.1090/S0002-9939-1975-0377189-1
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Abstract:
It is known that the scalar equation ${y^{(n)}} + {p_1}(t){y^{(n - 1)}} + \cdots + {p_n}(t)y = 0,t > 0,n > 1$, is eventually disconjugate if ${p_1}, \ldots ,{p_n}\epsilon C[0,\infty )$ and $\int {^\infty |{p_i}(t)|{t^{i - 1}}dt < \infty ,1 \leqslant i \leqslant n}$. This paper presents a weaker integral condition which also implies that the given equation is eventually disconjugate.References
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- W. A. Coppel, Stability and asymptotic behavior of differential equations, D. C. Heath and Company, Boston, Mass., 1965. MR 0190463
- G. Pólya, On the mean-value theorem corresponding to a given linear homogeneous differential equation, Trans. Amer. Math. Soc. 24 (1922), no. 4, 312–324. MR 1501228, DOI 10.1090/S0002-9947-1922-1501228-5
- D. Willett, Disconjugacy tests for singular linear differential equations, SIAM J. Math. Anal. 2 (1971), 536–545. MR 304772, DOI 10.1137/0502055
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 139-146
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0377189-1
- MathSciNet review: 0377189