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Comparison theorems for nonselfadjoint differential equations based on integral inequalities


Author: Kurt Kreith
Journal: Proc. Amer. Math. Soc. 34 (1972), 105-109
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1972-0304770-5
MathSciNet review: 0304770
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Abstract: In a variant of the classical Sturmian comparison theorem for selfadjoint Sturm-Liouville equations, A. Ju. Levin has replaced the pointwise conditions on the coefficients by an integral inequality. This theorem is generalized to apply to nonselfadjoint differential equations of the form

$\displaystyle u'' + b(x)u' + c(x)u = 0.$


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

  • [1] A. Ju. Levin, A comparison principle for second-order differential equations, Dokl. Akad. Nauk SSSR 135 (1960), 783-786 =Soviet Math. Dokl. 1 (1960), 1313-1316. MR 23 #A1875. MR 0124563 (23:A1875)
  • [2] E. Kamke, A new proof of Sturm's comparison theorems, Amer. Math. Monthly 46 (1939), 417-421. MR 1, 54. MR 0000326 (1:54d)
  • [3] C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc. 17 (1966), 611-616. MR 34 #1663. MR 0201781 (34:1663)
  • [4] K. Kreith, A comparison theorem for general elliptic equations with mixed boundary conditions, J. Differential Equations 8 (1970), 537-541. MR 0265737 (42:646)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0304770-5
Keywords: Comparison theorem, Riccati equations, integral equation
Article copyright: © Copyright 1972 American Mathematical Society

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