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A comparison theorem for the first nodal line of the solutions of quasilinear hyperbolic equations with non-increasing initial values

Published online by Cambridge University Press:  14 November 2011

Wu-Teh Hsiang  and
Man Kam Kwong
Wu-Teh Hsiang
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
Man Kam Kwong
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
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Synopsis

The oscillatory behaviour of quasilinear hyperbolic equations of the form

is studied using a Sturmian-type comparison theorem. We assume that for some function ψ′(x)≦0 and ψ′(x≦0.) The existence of the first nodal line of u is then inferred from the existence of that of the solution ν of

with .Some results of Pagan are improved using this approach and a problem posed by him is also studied.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 1-2 , 1980 , pp. 139 - 151
Copyright
Copyright © Royal Society of Edinburgh 1980

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References

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