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Nonlinear Oscillation of Fourth Order Differential Equations

Published online by Cambridge University Press:  20 November 2018

Takaŝi Kusano  and
Manabu Naito
Takaŝi Kusano
Affiliation:
Hiroshima University, Hiroshima, Japan
Manabu Naito
Affiliation:
Hiroshima University, Hiroshima, Japan
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In this paper we are concerned with the fourth order nonlinear differential equation

where the following conditions are always assumed to hold:

(a) r(t) is continuous and positive for t ≠ 0, and

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 4 , 01 August 1976 , pp. 840 - 852
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Atkinson, F. V., On second-order non-linear oscillations, Pacific. J. Math. 5 (1955), 643–647.Google Scholar
2. Belohorec, S., Oscillatory solutions of certain nonlinear differential equations of second order, Mat.-Fyz. Casopis Sloven. Akad. Vied. 11 (1961), 250–255. (Czech.)Google Scholar
3. Coffman, C. V. and Wong, J. S. W., Oscillation and nono sdilation theorems for second order ordinary differential equations, Funkcial. Ekvac. 15 (1972), 119–130.Google Scholar
4. Kiguradze, I. T., On the oscillation of solutions of the equation dmu/dtm + a(t)\u\n sign u = 0, Mat. Sb. 65 (1964), 172–187. (Russian.)Google Scholar
5. Kusano, T. and Naito, M., Nonlinear oscillation of second order differential equations with retarded argument, Ann. Mat. Pura Appl. (4) 106 (1975), 171–185.Google Scholar
6. Leighton, W. and Nehari, Z., On the oscillation of solutions of self-adjoint linear differential equations of the fourth order, Trans. Amer. Alath. Soc. 89 (1958), 325–377.Google Scholar
7. Levitan, B. M., Some problems of the theory of almost periodic functions I, Uspehi Mat. Nauk 2-5 (1947), 133–192. (Russian.)Google Scholar
8. Licko, L. and Svec, M., Le caractère oscillatoire des solutions de Vequation yn) -f- f(t)ya = 0, n > 1, Czechoslovak Math. J. 13 (1963), 481–491.+1,+Czechoslovak+Math.+J.+13+(1963),+481–491.>Google Scholar
9. Lovelady, D. L., An oscillation criterion for a fourth order integrally superlinear differential equation, to appear, Math. Systems Theory.Google Scholar
10. Macki, J. W. and Wong, J. S. W., Oscillation of solutions to second-order nonlinear differential equations, Pacific J. Math. 24 (1968), 111–117.Google Scholar
11. Nehari, Z., On a class of nonlinear second-order differential equations, Trans. Amer. Math. Soc. 95 (1960), 101–123.Google Scholar
12. Onose, H., Oscillatory properties of ordinary differential equations of arbitrary order, J. Differential Equations 7 (1970), 454–458.Google Scholar
13. Ryder, G. H. and Wend, D. V. V., Oscillation of solutions of certain ordinary differential equations of nth order, Proc. Amer. Math. Soc. 25 (1970), 463–469.Google Scholar
14. Terry, R. D. and Wong, P. K., Oscillatory properties of a fourth-order delay differential equation, Funkcial. Ekvac. 15 (1972), 209-220; 16 (1973), 213–224.Google Scholar
15. Wong, P. K., On a class of nonlinear fourth order differential equations, Ann. Mat. Pura Appl. 81 (1969), 331–346.Google Scholar