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A generalization of Sturm's separation theorem


Author: W. Allegretto
Journal: Proc. Amer. Math. Soc. 25 (1970), 151-154
MSC: Primary 35.11
DOI: https://doi.org/10.1090/S0002-9939-1970-0255959-3
MathSciNet review: 0255959
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Abstract: A Sturmian separation theorem is established for elliptic-parabolic equations with minimal assumptions on the coefficients and none on the regularity of the domain. A comparison theorem for linear equations and a separation theorem for quasi-linear equations are then obtained as applications.


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

  • [1] K. Kreith, Sturm theorems and positive resolvents, Trans. Amer. Math. Soc 139 (1969), 319-327. MR 0239246 (39:603)
  • [2] M. H. Protter, A comparison theorem for elliptic equations, Proc. Amer. Math. Soc. 10 (1959), 296-299. MR 21 #5803. MR 0107076 (21:5803)
  • [3] M. H. Protter and H. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 36 #2935. MR 0219861 (36:2935)
  • [4] 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)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0255959-3
Keywords: Sturmian separation theorem, comparison theorem, nonselfadjoint equations, elliptic-parabolic equations, quasi-linear equations
Article copyright: © Copyright 1970 American Mathematical Society

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