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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
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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