Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-19T08:21:48.478Z Has data issue: false hasContentIssue false

12.—Rotation Properties of Adjoint Pairs of Differential Systems

Published online by Cambridge University Press:  14 February 2012

Kurt Kreith
Affiliation:
University of California, Davis

Synopsis

A large class of self-adjoint fourth-order differential equations has the property that if one solution is oscillatory then all solutions are oscillatory. This paper establishes necessary and sufficient conditions for this property to hold for a corresponding class of non-self-adjoint differential equations.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1976

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

REFERENCES

1Leighton, W. and Nehari, Z.. On the oscillation of solutions of selfadjoint linear differential equations of the fourth order. Trans. Amer. Math. Soc. 89 (1958), 325377.CrossRefGoogle Scholar
2Ridenhour, J. and Sherman, T.. Conjugate points for fourth order linear differential equations. SIAMJ. Appl. Math. 22 (1972), 599603.CrossRefGoogle Scholar
3Schneider, L.. Oscillation properties of the 2–2 disconjugate fourth order selfadjoint differential equation. Proc. Amer. Math. Soc. 28 (1971), 545550.CrossRefGoogle Scholar
4Keener, M. S.. On oscillatory solutions of certain fourth order linear differential equations. SIAM J. Math. Anal. 3 (1972), 599605.CrossRefGoogle Scholar
5Kreith, K.. Nonselfadjoint fourth order differential equations with conjugate points. Bull. Amer. Math. Soc. 80 (1974), 11901192.CrossRefGoogle Scholar
6Kreith, K.. A dynamical criterion for conjugate points. Pacific J. Math., 58 (1975), 123132.CrossRefGoogle Scholar
7Kreith, K.. Rotation properties of a class of second order differential systems. J. Differential Equations 17 (1975), 395405.CrossRefGoogle Scholar
8Kreith, K.. A nonselfadjoint dynamical system. Proc. Edinburgh Math. Soc. 19 (1974), 7787.CrossRefGoogle Scholar