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Oscillation of Semilinear Elliptic Inequalities by Riccati Transformations

Published online by Cambridge University Press:  20 November 2018

E. S. Noussair  and
C. A. Swanson
E. S. Noussair
Affiliation:
University of New South Wales, Kensington, Australia
C. A. Swanson
Affiliation:
University of British Columbia, Vancouver, British Columbia
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A generalized Riccati transformation will be utilized to derive a Riccati-type inequality (3) associated with a semilinear elliptic inequality yL(y; x) ≦ 0 possessing a positive solution y in an exterior domain in Euclidean n-space. On the basis of (3), general sufficient conditions for the elliptic inequality to be oscillatory are developed in § 3. The matrix of coefficients of the second derivative terms in L(y;x) (i.e. (Aij) in (1)) is not restricted in any way beyond the usual ellipticity hypothesis (iv) below, and thereby one of the difficulties mentioned in [9] and inherent in the method there is resolved. Furthermore, the nonlinear term B﹛x, y) in (1) is not required to be one-signed.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 4 , April 1980 , pp. 908 - 923
Copyright
Copyright © Canadian Mathematical Society 1980

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