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Summability criteria for oscillation of second order linear differential equations

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Summary

Sufficient conditions involving summability methods are determined for oscillation of the equation y″+p(t)y=0. For example, if, for some positive integer\(k, \mathop \smallint \limits^t p\) is summable to + ∞ by the Cesàro mean of order k, then y″+p(t)y=0 is oscillatory.

References

  1. [1]

    W. J. Coles,An oscillation criterion for second-order linear differential equations, Proc. Amer. Math. Soc., 19 (1968), 755–759.

  2. [2]

    W. B. Fite,Concerning the z-ros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19 (1918), 341–352.

  3. [3]

    G. H. Hardy,Divergent Series, Oxford University Press, 1949.

  4. [4]

    P. Hartman,On nonoscillatory linear differential equations of second order, Amer. J. Math. 74 (1952), 389–400.

  5. [5]

    D. Willett,On the oscillatory behavior of the solutions of second order linear differential equations, Annales Polonici Math., 21 (1968).

  6. [6]

    A. Wintner,A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115–117.

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Supported by NASA Research Grant NGR-45-003-038.

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Coles, W.J., Willett, D. Summability criteria for oscillation of second order linear differential equations. Annali di Matematica 79, 391–398 (1968). https://doi.org/10.1007/BF02415185

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Keywords

  • Differential Equation
  • Positive Integer
  • Linear Differential Equation
  • Summability Method
  • Order Linear Differential Equation