On Kamenev-type oscillation theorems for second-order differential equations with damping

Journal of Mathematical Analysis and Applications

Volumn 258, Issue 1, 2001, Pages 244-257

  Wong, James S W ^a,b  

^a Chinney Investments Ltd   (Hong Kong)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Damping; Nonlinear; Ordinary differential equations; Oscillation; Second order

Indexed keywords

EID: 0001455794     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7376     Document Type: Article

References (31)

1. Atkinson F. V. On second order nonlinear oscillations. Pacific J. Math. 5:1955;643-647.
2. Baker J. W. Oscillation theorems for a second-order damped nonlinear differential equation. SIAM J. Appl. Math. 25:1973;37-40.
3. Bobisud L. E. Oscillation of nonlinear differential equations with small nonlinear damping. SIAM J. Appl. Math. 18:1970;74-76.
4. Bobisud L. E. Oscillation of solutions of damped nonlinear differential equations. SIAM J. Appl. Math. 18:1970;601-606.
5. Butler G. J. The oscillatory behavior of a second-order nonlinear differential equation with damping. J. Math. Anal. Appl. 57:1977;273-289.
6. Chen B.-S. Oscillation criteria for nonlinear second-order damped differential equations. Acta Math. Appl. Sinica. 15:1992;166-173.
7. Erbe L. Oscillation criteria for second-order nonlinear differential equations. Aunali di Mathematica Pura Appl. 94:1972;257-268.
8. Erbe L. H., Kong Q., Ruan S. Kamenev-type theorems for second-order matrix differential system. Proc. Amer. Math. Soc. 117:1993;957-962.
9. Fite W. B. Concerning the zeros of the solutions of certain differential equations. Trans. Amer. Math. Soc. 19:1918;341-352.
10. Grace S. R., Lalli B. S., Yeh C. C. Oscillation theorems for nonlinear second-order differential equations with a nonlinear damping term. SIAM J. Math. Anal. 15:1984;1082-1093.
11. Hartman P. On non-oscillatory linear differential equations of second order. Am. J. Math. 74:1952;389-400.
12. Kamenev I. V. An integral criterion for oscillation of linear differential equation of second order. Mat. Zametki. 23:1978;249-251.
13. n sgn u = 0. Casopis Pest. Mat. 89:1962;492-495.
14. Kwong M. K., Zettl A. Integral inequalities and second-order linear oscillation. J. Diff. Eq. 45:1982;16-33.
15. Leighton W. The detection of oscillation of solutions of a second-order linear differential equation. Duke Math. J. 17:1950;57-62.
16. Naito M. Oscillation criteria for a second-order differential equation with a damping term. Hiroshima Math. J. 4:1974;347-354.
17. Philos Ch. G. On a Kamenev’s integral criterion for oscillation of linear differential equations of second order. Utilitas Math. 24:1983;277-289.
18. Philos Ch. G. Oscillation theorems for linear differential equations of second order. Arch. Math. 53:1989;482-492.
19. Sobol I. M. Investigation with the aid of polar coordinates of the asymptotic behavior of solutions of a linear differential equation of the second order. Math. Sb. 28:1951;707-714.
20. Wintner A. A criterion of oscillatory stability. Q. J. Appl. Math. 7:1949;115-117.
21. Wong J. S. W. Oscillation and nonoscillation of solutions of second-order linear differential equations with integrable coefficients. Trans. Amer. Math. Soc. 144:1969;197-215.
22. Wong J. S. W. Oscillation theorems for second-order nonlinear differential equations. Bull. Inst. Math. Acad. Sinica. 3:1975;283-309.
23. Wong J. S. W. An oscillation criterion for second-order nonlinear differential equations with iterated integral averages. Diff. Int. Eq. 6:1993;83-91.
24. Wong J. S. W. Oscillation criteria for second-order nonlinear differential equations involving general means. J. Math. Anal. Appl. 247:2000;489-505.
25. Wong J. S. W., Yeh C. C. An oscillation criterion for second-order sublinear differential equations. J. Math. Anal. Appl. 171:1992;346-351.
26. Wong R. Asymptotic Approximations of Integrals. 1989;Academic Press, New York.
27. Yan Jurang. A note on an oscillatory criterion for an equation with damped term. Proc. Amer. Math. Soc. 90:1984;277-280.
28. Yan Jurang. Oscillation theorems for second-order linear differential equations with damping. Proc. Amer. Math. Soc. 98:1986;276-282.
29. Yeh C. C. Oscillation theorems for nonlinear second-order differential equations with a damped term. Proc. Amer. Math. Soc. 84:1982;397-402.
30. Yelchin M. Sur le condition pour q’une solution d’un systéme linéaire du second ordre posséde deux zeros. Dokl. Akad. Nauk SSSR. 51:1946;573-576.
31. Zlámal M. Oscillation criterions. Casopis Pest. Mat. 75:1950;213-217.