Some oscillation properties of selfadjoint elliptic equations
Author:
V. B. Headley
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
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Abstract | References | Similar Articles | Additional Information
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 ${R^n}$.
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- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
- I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Israel Program for Scientific Translations, Jerusalem, 1965; Daniel Davey & Co., Inc., New York, 1966. Translated from the Russian by the IPST staff. 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 https://doi.org/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 https://doi.org/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
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Additional Information
Keywords:
Nonoscillation theorems,
elliptic partial differential equations,
unbounded <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$n$">-dimensional domains,
comparison theorem,
separation theorem,
oscillatory equation,
Schrodinger operator
Article copyright:
© Copyright 1970
American Mathematical Society