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A property of $ y'''+p(x)y\sp{'} +{1\over 2}p\sp{'} (x)y=0$

Author: Gary D. Jones
Journal: Proc. Amer. Math. Soc. 33 (1972), 420-422
MSC: Primary 34C10
MathSciNet review: 0293170
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Abstract: It is shown that if $ y''' + p(x)y' + \tfrac{1}{2}p'(x)y = 0$ has an oscillatory solution, it has bases with 0, 1, 2, or 3 oscillatory elements.

References [Enhancements On Off] (What's this?)

  • [1] G. D. Birkhoff, On solutions of ordinary linear homogeneous differential equations of the third order, Ann. of Math. 12 (1911), 103-127. MR 1503560
  • [2] Walter Leighton, Ordinary differential equations, 2nd ed., Wadsworth, Belmont, Calif., 1966. MR 33 #5973. MR 0197810 (33:5973)
  • [3] W. R. Utz, Oscillating solutions of third order differential equations, Proc. Amer. Math. Soc. 26 (1970), 273-276. MR 41 #7208. MR 0262602 (41:7208)

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Keywords: Differential equations, third order, oscillation, selfadjoint
Article copyright: © Copyright 1972 American Mathematical Society

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