Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T18:01:47.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillation criteria for second order hyperbolic initial value problems

Published online by Cambridge University Press:  14 November 2011

Gordon Pagan  and
David Stocks
Gordon Pagan
Affiliation:
Department of Mathematics and Ballistics, Royal Military College of Science, Shrivenham
David Stocks
Affiliation:
Department of Mathematics and Ballistics, Royal Military College of Science, Shrivenham
Get access Rights & Permissions [Opens in a new window]

Synopsis

It is established that under certain restrictions the solution u of the equation uxy − gu = 0 satisfying u(x, 0) = p(x) and u(0,y) = q(y) in ([0, = ∞) × [0, ∞), changes sign in where (X, Y) is any point in the relevant region.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 83 , Issue 3-4 , 1979 , pp. 239 - 244
Copyright
Copyright © Royal Society of Edinburgh 1979

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Garabedian, P. R.. Partial differential equations (New York: Wiley, 1964).Google Scholar
2Travis, C. C.. Comparison and oscillation theorems for hyperbolic equations. Utilitas Math. 6 (1974), 139–151.Google Scholar
3Kahane, C.. Oscillation theorems for solutions of hyperbolic equations. Proc. Amer. Math. Soc. 41 (1973), 183–188.CrossRefGoogle Scholar
4Kreith, K.. Sturmian theorems for hyperbolic equations. Proc. Amer. Math. Soc. 22 (1969), 277–281.Google Scholar
5Kreith, G.. Surmian theorems for characteristic initial value problems. Arti Accad. Naz. Lincei Rend. Ci Sci. Fis. Mat. Natur. 47 (1969), 139–144.Google Scholar
6Pagan, G.. Oscillation theorems for characteristic initial value problems for linear hyperbolic equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur 55 (1973), 301–313.Google Scholar
7Pagan, G.. Existence of nodal lines for solutions of hyperbolic equations. Amer. Math. Monthly 83 (1976), 358–359.CrossRefGoogle Scholar
8Pagan, G.. An oscillation theorem for characteristic initial value problems in linear hyperbolic equations. Proc. Roy. Soc. Edinburgh Sect. A 77, (1977), 265–271.CrossRefGoogle Scholar
9Pagan, G.. The study of the oscillatory behaviour of solutions of hyperbolic partial differential equations. (Doctoral thesis, Chelsea College, Univ. Lond., 1975).Google Scholar