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An oscillation theorem for characteristic initial value problems in linear hyperbolic equations†

Published online by Cambridge University Press:  14 February 2012

Gordon Pagan
Gordon Pagan
Affiliation:
Department of Mathematics and Ballistics, Royal Military College of Science, Shrivenham
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Synopsis

It is established that under certain restrictions the solution u of the characteristic initial value problem uxy+g(x, y)u = 0, u(x, 0) = p(x) and u(0, y) = q(y), where p(x) > 0 and q(y) > 0, in [0, ∞) x [0, ∞) changes sign along a monotonic decreasing curve which is asymptotic to the axes.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 3-4 , 1977 , pp. 265 - 271
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Garabedian, P. R.. Partial differential equations (New York: Wiley, 1964).Google Scholar
2Pagan, G.. Oscillation theorems for characteristic initial value problems for linear hyperbolic equations. Rend. Accad. Naz. Lincei Sci. Fis. Mat. Nat. 55 (1973), 301–313.Google Scholar
3Kreith, K.. Sturmian theorems for characteristic initial value problems. Rend. Accad. Naz. Lincei Sci. Fis. Mat. Nat. 47 (1969), 139–144.Google Scholar
4Courant, R.. Differential and integral calculus, 1 (Glasgow: Blackie, 1952)Google Scholar