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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Oscillation properties of two term linear differential equations

Author: G. A. Bogar
Journal: Trans. Amer. Math. Soc. 161 (1971), 25-33
MSC: Primary 34.42
MathSciNet review: 0284646
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Abstract: The two term differential equations $ {L_n}[y] + py = 0$, where $ {L_0}[y] = y,{L_i}[y] = ({\rho _i}(t){L_i}[y(t)])'$, were recently studied by Z. Nehari. In this paper we give integral conditions which assure the integrability of $ \rho _1^{ - 1}(t)p(t)$ on $ [a,\infty )$ when $ {L_n}[y]$ is disconjugate. By changing the integral conditions slightly we then prove that the equation has n linearly independent oscillatory solutions.

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Keywords: Nonoscillatory equations, disconjugate, oscillatory solution, fundamental set of solutions, iterated integrals, Green's function
Article copyright: © Copyright 1971 American Mathematical Society

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