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The existence of conjugate points for selfadjoint differential equations of even order


Author: Roger T. Lewis
Journal: Proc. Amer. Math. Soc. 56 (1976), 162-166
DOI: https://doi.org/10.1090/S0002-9939-1976-0399576-9
MathSciNet review: 0399576
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Abstract | References | Additional Information

Abstract: This paper presents sufficient conditions on the coefficents of $ {L_{2n}}y = \Sigma _{k = 0}^n{( - 1)^{n - k}}{({p_k}{y^{(n - k)}})^{(n - k)}}$ which insure that $ {L_{2n}}y = 0$ has conjugate points $ \eta (a)$ for all $ a > 0$. The main theorem implies that $ {( - 1)^n}{y^{(2n)}} + py = 0$ has conjugate points $ \eta (a)$ for all $ a > 0$ when $ {\smallint ^\infty }{x^\alpha }p(x)dx = - \infty $ for some $ \alpha < 2n - 1$ with no sign restrictions on $ p(x)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0399576-9
Keywords: Selfadjoint linear differential equations of even order, oscillation, conjugate points
Article copyright: © Copyright 1976 American Mathematical Society

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