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 | References | Similar Articles | Additional Information
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.
- Kurt Kreith, Sturmian theorems and positive resolvents, Trans. Amer. Math. Soc. 139 (1969), 319–327. MR 239246, DOI https://doi.org/10.1090/S0002-9947-1969-0239246-1
- M. H. Protter, A comparison theorem for elliptic equations, Proc. Amer. Math. Soc. 10 (1959), 296–299. MR 107076, DOI https://doi.org/10.1090/S0002-9939-1959-0107076-6
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
- C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc. 17 (1966), 611–616. MR 201781, DOI https://doi.org/10.1090/S0002-9939-1966-0201781-2
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Additional Information
Keywords:
Sturmian separation theorem,
comparison theorem,
nonselfadjoint equations,
elliptic-parabolic equations,
quasi-linear equations
Article copyright:
© Copyright 1970
American Mathematical Society