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On the oscillation of solutions of linear differential equations

Part of: Qualitative theory

Published online by Cambridge University Press:  26 February 2010

B. J. Harris
B. J. Harris
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115-2888, U.S.A.
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Extract

We consider the second order linear differential equation

where p and q are real-valued and p(t) > 0 for all t ≥ T. Our interest here is the oscillatory nature of solutions of (1.1). More particularly we consider the following questions, (I), (II) and (III).

MSC classification

Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 214 - 226
Copyright
Copyright © University College London 1984

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References

1.Atkinson, F. V.. On second order linear oscillations. Revista, Serie A, Mat. y Fis. Tedr. (Tucumàn), 8 (1951), 71–87.Google Scholar
2.Erbe, L.. Oscillation theorems for second order linear differential equations. Pacific J. Math., 35 (1970), 337–343.Google Scholar
3.Harris, B. J.. On the zeros of solutions of differential equations. J. London Math. Soc. (2), 27 (1983), 447–464.CrossRefGoogle Scholar
4.Hartman, P.. Ordinary differential equations (Wiley, New York, 1964).Google Scholar
5.Knowles, I.. Stability conditions for second order linear differential equations. J. Diff. Equations, 34 (1979), 179–203.Google Scholar
6.Kuptsov, N. P.. Conditions of non self-adjointness of a second order linear differential operator. Dokl. Akad. Nauk. SSSR, 138 (1961), 767–770.Google Scholar
7.Kwong, M. K.. On certain comparison theorems for second order linear oscillation. Proc. Amer. Math. Soc, 84 (1982), 539–542.CrossRefGoogle Scholar
8.Kwong, M. K.. On certain Riccati integral equations and second order linear oscillation. J. Math. Anal. Appl, 85 (1982), 315–330.Google Scholar
9.Kwong, M. K. and Zettl, A.. Differential and integral inequalities and second order linear oscillations. J. Diff. Equations, 45 (1982), 16–23.Google Scholar
10.Kwong, M. K. and Zettl, A.. Asymptotically constant functions and second order linear oscillation. J. Math. Anal. Appl, 93 (1983), 475–493.Google Scholar
11.Swanson, C. A.. Comparison and oscillation theory of linear differential equations (Academic Press, New York and London, 1968).Google Scholar