Summability criteria for oscillation of second order linear differential equations

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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.


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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).

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