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A Kneser Theorem for Higher order Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

W. Allegretto
W. Allegretto*
Affiliation:
University of Alberta
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The problem of establishing oscillation and non-oscillation criteria for elliptic equations has recently been considered by several authors. Extensive bibliographies may be found in the books by C. A. Swanson, [7], and by K. Kreith, [3].

Most of the interest has so far centered on equations of second order with some results also established for fourth order equations. Non-oscillation theorems for higher order equations have recently been established by the author, [1], and by Noussair and Yoshida, [5]. In particular, both in [1] and [5], Kneser-type theorems were established for classes of higher order elliptic equations.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 1 , 01 March 1977 , pp. 1 - 8
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Allegretto, W., Nonoscillation theory of elliptic equations of order 2n, Pacific J. Math., 64 (1976), 1-16.Google Scholar
2. Friedman, A., Partial differential equation, Holt, Rinehart and Winston, Inc., New York 1969.Google Scholar
3. Kreith, K., Oscillation theory, Lecture Notes in Mathematics, Vol. 324, Springer-Verlag, Berlin 1973.Google Scholar
4. Noussair, E. S., Oscillation theory of elliptic equations of order 2m, J. Differential Equations 10 (1971), 100-111. MR43, #6564.Google Scholar
5. Noussair, E. and Yoshida, N., Nonoscillation criteria for elliptic equations of order 2 m, submitted for publication.Google Scholar
6. Rellich, F., Perturbation theory of eigenvalue problems, Gordon and Breach, New York 1969. MR39, #2014.Google Scholar
7. Swanson, C. A., Comparison and oscillation theory of linear differential equations Academic Press, New York and London, 1968.Google Scholar