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A Note on a Comparison Result for Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

W. Allegretto
W. Allegretto*
Affiliation:
University of A Iberta, Edmonton, Alberta
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In a recent paper [2], Bushard established and applied a comparison theorem for positive solutions to the equation:

in an arbitrary bounded domain D of Euclidean w-space Rn. The proof of these results depended on the absence of mixed derivatives of u in the equation considered.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 1081 - 1085
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Allegretto, W., A comparison theorem for nonlinear operators, Ann. Scuola Norm. Sup. Pisa (1) 25 (1971), 41–46.Google Scholar
2. Bushard, L. B., A comparison result for a class of quasilinear elliptic partial differential equations, J. Differential Equations 21 (1976), 439–443.Google Scholar
3. Sternberg, S., Lectures on differential geometry (Prentice-Hall, New Jersey, 1964).Google Scholar
4. Swanson, C. A., Comparison and oscillation theory of linear differential equations (Academic Press, New York and London, 1968).Google Scholar