Some oscillation properties of selfadjoint elliptic equations
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- by V. B. Headley
- Proc. Amer. Math. Soc. 25 (1970), 824-829
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259323-2
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Abstract:
In this paper a method is given for generalizing to partial differential equations known nonoscillation theorems for second order ordinary differential equations. As illustrations, two theorems of Hille (one of integral type and one of limit type) are generalized to obtain nonoscillation criteria for second order linear elliptic differential equations on unbounded domains $G$ in $n$-dimensional Euclidean space ${R^n}$.References
- Colin Clark and C. A. Swanson, Comparison theorems for elliptic differential equations, Proc. Amer. Math. Soc. 16 (1965), 886–890. MR 180753, DOI 10.1090/S0002-9939-1965-0180753-X
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
- I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Daniel Davey & Co., Inc., New York, 1966. Translated from the Russian by the IPST staff; Israel Program for Scientific Translations, Jerusalem, 1965. MR 0190800
- V. B. Headley and C. A. Swanson, Oscillation criteria for elliptic equations, Pacific J. Math. 27 (1968), 501–506. MR 236502
- Einar Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234–252. MR 27925, DOI 10.1090/S0002-9947-1948-0027925-7
- Walter Leighton, On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37–47. MR 46506, DOI 10.1112/jlms/s1-27.1.37
- Ruth Lind Potter, On self-adjoint differential equations of second order, Pacific J. Math. 3 (1953), 467–491. MR 56156
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 824-829
- MSC: Primary 35.11; Secondary 34.00
- DOI: https://doi.org/10.1090/S0002-9939-1970-0259323-2
- MathSciNet review: 0259323