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Oscillation theorems for semilinear hyperbolic and ultrahyperbolic operators

The oscillation property of the semilinear hyperbolic or ultra-hyperbolic operator L defined by is studied. Sufficient conditions are provided for all solutions of uL[u] ≤ 0 satisfying certain boundary conditions to be oscillatory. The basis of our results is the non-existence of positive solutions...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 1978-02, Vol.18 (1), p.55-64
Main Author: Narita, Mamoru
Format: Article
Language:English
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Summary:The oscillation property of the semilinear hyperbolic or ultra-hyperbolic operator L defined by is studied. Sufficient conditions are provided for all solutions of uL[u] ≤ 0 satisfying certain boundary conditions to be oscillatory. The basis of our results is the non-existence of positive solutions of the associated differential inequalities.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700007802