Oscillation criteria for second-order half-linear ordinary differential equations with damping

Rocky Mountain Journal of Mathematics

Volumn 33, Issue 3, 2003, Pages 927-951

  Li, Wan Tong ^a   Zhong, Cheng Kui ^a   Fan, Xian Ling ^a  

^a LANZHOU UNIVERSITY   (China)

Author keywords

Damping; Half linear differential equations; Oscillation; Second order

Indexed keywords

EID: 1642303377     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/rmjm/1181069936     Document Type: Article

References (45)

1. J.W. Baker, Oscillation theorems for a second order damped nonlinear differ-ential equation, SIAM J. Math. Anal. 25 (1973), 37-40.
2. L.E. Bobisud, Oscillation of Solutions of damped nonlinear differential equa-tions, SIAM J. Math. Anal. 18 (1970), 601-606.
3. G.J. Butler, The oscillatory behavior of a second order nonlinear differential equation with damping, J. Math. Anal. Appl. 57 (1977), 273-289.
4. p-2x = 0, p> 1, Houston J. Math. 17 (1991), 63-70.
5. O. Dosly, A remark on half-linear extension of the Hartman-Wintner the-orem, Fourth Mississippi State Conf. on Differential Equations and Computation Simulations, Electronic J. Differential Equations, Conf. 03, 1999, pp. 29-37.
6. A. Elbert, A half-linear second order differential equation, in Qualitative theory of differential equations, Colloq. Math. Soc. Janos Bolyai, vol. 30, Szeged, 1979, pp. 153-180.
7. A. Elbert, Oscillation and nonoscillation theorems for nonlinear ODE, Lecture Notes in Math., vol. 964, Springer, New York, 1992.
8. S.R. Grace, Oscillation theorems for second order nonlinear differential equations with damping, Math. Nachr. 141 (1989), 117-127.
9. S.R. Grace, Oscillation criteria for second order nonlinear differential equations with damping, J. Austral. Math. Soc. Ser. A 49 (1990), 43-54.
10. S.R. Grace, Oscillation theorems for nonlinear differential equations of second order, J. Math. Anal. Appl. 171 (1992), 220-241.
11. S.R. Grace Oscillation theorems for certain second order perturbed nonlinear differential equations, J. Math. Anal. Appl. 77 (1980), 205-214.
12. S.R. Grace and B.S. Lalli, Integral averaging technique for oscillation of second order nonlinear differential equations, J. Math. Anal. Appl. 149 (1990), 277-311.
13. S.R. Grace and B.S. Lalli, Oscillation theorems for second order superlinear differential equations with damping, J. Austral. Math. Soc. Ser. A 53 (1992), 156-165.
14. S.R. Grace, B.S. Lalli and C.C. Yeh, Oscillation theorems for nonlinear second order differential equations with a nonlinear damping term, SIAM J. Math. Anal. 15 (1984), 1082-1093.
15. S.R. Grace, B.S. Lalli and C.C. Yeh, Addendum: Oscillation theorems for nonlinear second order differ ential equations with a nonlinear damping term, SIAM J. Math. Anal. 19 (1988), 1252-1253.
16. G.H. Hardy, J.E. Litlewood and G. Polya, Inequalities, 2nd ed., Cambridge University Press, Cambridge, 1988.
17. B.J. Harris, On the oscillation of solutions of linear differential equations, Mathematica 33 (1984), 214-226.
18. P. Hartman, On nonoscillatory linear differential equations of second order, Amer. J. Math. 74 (1952), 389-400.
19. H.L. Hong, W.C. Lian and C.C. Yeh, The oscillation of half-linear differential equations with an oscillatory coefficient, Math. Comput. Modelling 24 (1996), 77-86.
20. H.B. Hsu and C.C. Yeh, Oscillation theorems for second order half-linear differential equations, Appl. Math. Lett. 9 (1996), 11-11.
21. I.V. Kamenev, Integral criteria of linear differential equations of second order, Mat. Zametki 23 (1978), 249-251.
22. N. Kandelaki, A. Lomtatidze and D. Ugulava, Oscillation and nonoscillation criteria of a second order half-linear equation, Georgian Math. J. 7 (2000), 1-19.
23. Q. Kong, Interval criteria for oscillation of second-order linear ordinary differential equations, J. Math. Anal. Appl. 229 (1999), 258-270.
24. Q. Kong, Oscillation criteria for second order half-linear differential equations, Fields Institute Communications, vol. 21, 1999, pp. 317-323.
25. H.J. Li, Oscillation criteria for second order linear differential equations, J. Math. Anal. Appl. 194 (1995), 217-234.
26. H.J. Li and C.C. Yeh, Sturmian comparison theorem for half-linear second-order differential equations, Proc. Royal Soc. Edinburgh 125A (1995), 1193-1204.
27. H.J. Li and C.C. Yeh, Oscillation of half-linear second order differential equations, Hi roshima Math. J. 25 (1995), 584-596.
28. W.T. Li, Oscillation of certain second-order nonlinear differential equations, J. Math. Anal. Appl. 217 (1998), 1-14.
29. W.T. Li, Positive solutions of second order nonlinear differential equations, J. Math. Anal. Appl. 221 (1998), 326-337.
30. W.T. Li and R.P. Agarwal, Interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations, J. Math. Anal. Appl. 245 (2000), 171-188.
31. W.T. Li and R.P. Agarwal, Interval oscillation criteria for second order nonlinear differential equations with damping, Comput. Math. Appl. 40 (2000), 217-230.
32. W.T. Li and R.P. Agarwal, Interval oscillation criteria for a forced nonlinear ordinary differen tial equation, Appl. Anal. 75 (2000), 341-347.
33. W.T. Li, M.Y. Zhang and X.L. Fei, Oscillation criteria for second order nonlinear differential equations with damped term, Indian J. Pure Appi. Math. 30 (1999), 1017-1029.
34. W.C. Lian, C.C. Yeh and H.J. Li, The distance between zeros of an oscillatory solution to a half-linear differential equation, Comput. Math. Appl. 29 (1995), 39-43.
35. J.V. Manojlovic, Oscillation criteria for second-order half-linear differential equations, Math. Comput. Modelling 30 (1999), 109-119.
36. J.D. Mirzov, On some analogs of Sturm’s and Kneser’s theorems for nonlinear systems, J. Math. Anal. Appl. 54 (1976), 418-425.
37. Ch.G. Philos, Oscillation theorems for linear differential equations of second order, Arch. Math. (Basel) 53 (1989), 482-492.
38. Yu.V. Rogovchenko, Oscillation criteria for second order nonlinear perturbed differential equations, J. Math. Anal. Appl. 215 (1997), 334-357.
39. Yu V, Oscillation theorems for second order equations with damping, Nonlinear Anal. 41 (2000), 1005-1028.
40. A. Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115-117.
41. J.R. Yan, A note on an oscillation criterion for an equation with damped term, Proc. Amer. Math. Soc. 90 (1984), 277-280.
42. J.R. Yan, Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc. 98 (1986), 276-282.
43. C.C. Yeh, Oscillation theorems for nonlinear second order differential equations with damping term, Proc. Amer. Math. Soc. 84 (1982), 397-402.
44. P.J.Y. Wong and R.P. Agarwal, Oscillatory behavior of solutions of certain second order nonlinear differential equations, J. Math. Anal. Appl. 198 (1996), 337-354.
45. P.J.Y. Wong and R.P. Agarwal, Oscillation theorems and existence criteria of asymptotically mono tone solutions for second order differential equations, Dynamic Systems Appl. 4 (1995), 477-496.