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Strong Oscillation of Elliptic Equations in General Domains

Published online by Cambridge University Press:  20 November 2018

C. A. Swanson
C. A. Swanson*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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Strong oscillation criteria will be obtained for the linear elliptic partial differential equation

(1)

in unbounded domains R of general type in n-dimensional Euclidean space En. It will be assumed throughout that B and each Aij are real-valued continuous functions in R, and that the matrix (Aij(x)) is symmetric and positive definite in R.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 105 - 110
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Courant, R., and Hilbert, D., Methods of mathematical physics I, Wiley, New York, 1953.Google Scholar
2. Glazman, I.M., On the negative part of the spectrum of one-dimensional and multi-dimensional differential operators on vector-functions, Dokl. Akad. Nauk SSSR. 119 (1958), 421–424.Google Scholar
3. Headley, V.B., and Swanson, C.A., Oscillation criteria for elliptic equations, Pacific J. Math. 27 (1968), 501–506.Google Scholar
4. Kreith, Kurt, Oscillation theorems for elliptic equations, Proc. Amer. Math. Soc. 15 (1964), 341–344.Google Scholar
5. Kreith, Kurt, and Travis, Curtis C., Oscillation criteria for self adjoint elliptic equations (to appear).Google Scholar
6. Swanson, C.A., An identity for elliptic equations with applications, Trans. Amer. Math. Soc. 134 (1968), 325–333.Google Scholar
7. Swanson, C.A., Comparison and oscillation theory of linear differential equations, Mathematics in Science and Engineering, Vol. 48, Academic Press, New York, 1968.Google Scholar