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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Oscillation properties of perturbed disconjugate equations
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by William F. Trench PDF
Proc. Amer. Math. Soc. 52 (1975), 147-155 Request permission

Abstract:

Oscillation conditions are given for the equation ${L_u} + f(t,u) = 0$, where \[ Lu = \frac {1} {{{\beta _n}}}\frac {d} {{dt}}\frac {1} {{{\beta _{n - 1}}}} \cdots \frac {d} {{dt}}\frac {1} {{{\beta _1}}}\frac {d} {{dt}}\frac {u} {{{\beta _0}}}(n \geqslant 2),\] with ${\beta _0}, \ldots ,{\beta _n}$ positive and continuous on $(0,\infty ),\int {^\infty {\beta _i}dt = \infty (1 \leqslant i \leqslant n - 1)}$, and $f$ subject to conditions which include $uf(t,u) \geqslant 0$. The results obtained include previously known oscillation conditions for the equation ${u^{(n)}} + f(t,u) = 0$ for both linear and nonlinear cases.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 147-155
  • MSC: Primary 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0379987-7
  • MathSciNet review: 0379987