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Published online by Cambridge University Press: 14 November 2011
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.