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Linear differential equations where nonoscillation is equivalent to eventual disconjugacy


Author: Jerry R. Ridenhour
Journal: Proc. Amer. Math. Soc. 49 (1975), 366-372
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1975-0364759-X
MathSciNet review: 0364759
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Abstract: Conditions on $ n$th order linear differential equations are given which imply that nonoscillation is equivalent to eventual disconjugacy. These conditions are in the form of assumptions that certain boundary-value functions are infinite for all values of the argument.


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  • [1] G. B. Gustafson, The nonequivalence of oscillation and nondisconjugacy, Proc. Amer. Math. Soc. 25 (1970), 254-260. MR 44 #1872. MR 0284648 (44:1872)
  • [2] -, Eventual disconjugacy of self-adjoint fourth order linear differential equations, Proc. Amer. Math. Soc. 35 (1972), 187-192. MR 45 # 7178. MR 0298126 (45:7178)
  • [3] M. Hanan, Oscillation criteria for third-order linear differential equations, Pacific J. Math. 11 (1961), 919-944. MR 26 #2695. MR 0145160 (26:2695)
  • [4] M. S. Keener, Oscillatory solutions and multi-point boundary value functions for certain $ n$th-order linear ordinary differential equations, Pacific J. Math. 51 (1974), 187-202. MR 0352609 (50:5096)
  • [5] -, On the equivalence of oscillation and the existence of infinitely many conjugate points, Rocky Mountain J. Math. 5 (1975), 125-134. MR 0357972 (50:10437)
  • [6] W. Leighton and Z. Nehari, On the oscillation of solutions of selfadjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325-377. MR 21 #1429. MR 0102639 (21:1429)
  • [7] Z. Nehari, Disconjugate linear differential operators, Trans. Amer. Math. Soc. 129 (1967), 500-516. MR 36 #2860. MR 0219781 (36:2860)
  • [8] J. R. Ridenhour, On the zeros of solutions of $ n$th order linear differential equations, J. Differential Equations 16 (1974), 45-71. MR 0364758 (51:1012)
  • [9] T. L. Sherman, Properties of solutions of $ n$th order linear differential equations, Pacific J. Math. 15 (1965), 1045-1060. MR 32 #2654. MR 0185185 (32:2654)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0364759-X
Keywords: Linear differential equations, oscillation, nonoscillation, conjugacy, disconjugacy, eventual disconjugacy, $ k$th conjugate point, extremal solutions, boundary-value functions, distributions of zeros
Article copyright: © Copyright 1975 American Mathematical Society

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