Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T02:10:50.629Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillation criteria for third order hyperbolic characteristic initial value problems

Published online by Cambridge University Press:  14 November 2011

C. C. Travis  and
Norio Yoshida
C. C. Travis
Affiliation:
Technology Assessments Section, Health and Safety Research Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, U.S.A.
Norio Yoshida
Affiliation:
Department of Mathematics, Faculty of Engineering, Iwate University, Morioka, Japan
Get access Rights & Permissions [Opens in a new window]

Synopsis

Sufficient conditions for oscillation of solutions to third order hyperbolic characteristic initial value problems are established. The results generalize known oscillation criteria for second order hyperbolic problems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 1-2 , 1981 , pp. 135 - 140
Copyright
Copyright © Royal Society of Edinburgh 1981

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

1Kartsatos, A. G.. On nth order differential inequalities. J. Math. Anal. Appl. 52 (1975), 1–9.CrossRefGoogle Scholar
2Kiguradze, I. T.. Oscillation properties of solutions of certain ordinary differential equations. Dokl. Akad. Nauk SSSR 144 (1962), 33–36. (Russian) = Soviet Math. Dokl. 3 (1962), 649–652.Google Scholar
3Kreith, K.. Sturtnian theorems for characteristic initial value problems. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 47 (1969), 139–144.Google Scholar
4Ličko, I. and Švec, M.. Le caractère oscillatoire des solutions de l'équation y(n) + f(x)y∝ = 0, n > 1. Czechoslovak Math. J. 13 (1963), 481–491. 1' href=https://dx.doi.org/10.21136/CMJ.1963.100581>CrossRef 1' href=https://scholar.google.com/scholar_lookup?title=Le+caract%C3%A8re+oscillatoire+des+solutions+de+l'%C3%A9quation+y(n)+%2B+f(x)y%E2%88%9D+%3D+0%2C+n+%3E+1&author=Li%C4%8Dko+I.&author=%C5%A0vec+M.&publication+year=1963&journal=Czechoslovak+Math.+J.&volume=13&doi=10.21136%2FCMJ.1963.100581&pages=481-491>Google Scholar
5Mikusiński, J.. On Fite's oscillation theorems. Colloq. Math. 2 (1951), 34–39.CrossRefGoogle Scholar
6Okikiolu, G. O., Aspects of the Theory of Bounded Integral Operators in Lp-spaces (New York: Academic Press, 1971).Google Scholar
7Onose, H.. A comparison theorem and the forced oscillation. Bull. Austral. Math. Soc. 13 (1975), 13–19.CrossRefGoogle Scholar
8Pagan, 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
9Pagan, 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
10Pagan, G. and Stocks, D.. Oscillation criteria for second order hyperbolic initial value problems. Proc. Roy. Soc. Edinburgh Sect. A 83 (1979), 239–244.CrossRefGoogle Scholar
11Yoshida, N.. An oscillation theorem for characteristic initial value problems for nonlinear hyperbolic equations. Proc. Amer. Math. Soc. 76 (1979), 95–100.CrossRefGoogle Scholar