Geodesic
Oscillations of Second Order Neutral Differential Equations
Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 485-496

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we consider the oscillatory behavior of the second order neutral delay differential equation where t ≥ t0,T and σ are positive constants, a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.
DOI : 10.4153/CMB-1993-064-4
Mots-clés : 34K15, 34C10, 34K25 
Ruan, Shigui. Oscillations of Second Order Neutral Differential Equations. Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 485-496. doi: 10.4153/CMB-1993-064-4
@article{10_4153_CMB_1993_064_4,
     author = {Ruan, Shigui},
     title = {Oscillations of {Second} {Order} {Neutral} {Differential} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {485--496},
     year = {1993},
     volume = {36},
     number = {4},
     doi = {10.4153/CMB-1993-064-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-064-4/}
}
TY  - JOUR
AU  - Ruan, Shigui
TI  - Oscillations of Second Order Neutral Differential Equations
JO  - Canadian mathematical bulletin
PY  - 1993
SP  - 485
EP  - 496
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-064-4/
DO  - 10.4153/CMB-1993-064-4
ID  - 10_4153_CMB_1993_064_4
ER  - 
%0 Journal Article
%A Ruan, Shigui
%T Oscillations of Second Order Neutral Differential Equations
%J Canadian mathematical bulletin
%D 1993
%P 485-496
%V 36
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-064-4/
%R 10.4153/CMB-1993-064-4
%F 10_4153_CMB_1993_064_4

[1] 1. Erbe, L. H., Kong, Q. and Ruan, S., Kamenev type theorems for second order matrix differential systems, Proc. Amer. Math. Soc. 117(1993), 957–962. Google Scholar

[2] 2. Erbe, L. H. and Zhang, B. G., Oscillation of second order neutral differential equations, Bull. Austral. Math. Soc. 32(1989), 79–90. Google Scholar

[3] 3. Fife, B., Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19(1918), 341–352. Google Scholar

[4] 4. Grace, S. R. and Lalli, B. S., Oscillations of nonlinear second order neutral delay differential equations, Rat. Mat. 3(1987), 77–84. Google Scholar

[5] 5. Grace, S. R. and Lalli, B. S., Oscillation and asymptotic behavior of certain second order neutral differential equations, Rat. Mat. 5(1989), 121–126. Google Scholar

[6] 6. Graef, J. R., Grammatikopoulos, M. K. and Spikes, P. W., Asymptotic properties of solutions of nonlinear delay differential equations of the second order, Rat. Mat. 4(1988), 133–149. Google Scholar

[7] 7. Graef, J. R., Grammatikopoulos, M. K. and Spikes, P. W., On the asymptotic behavior of solutions of a second order nonlinear neutral delay differential equation, J. Math. Anal. Appl. 156(1991), 23–39. Google Scholar

[8] 8. Grammatikopoulos, M. K., Ladas, G. and Meimaridou, A., Oscillations of second order neutral delay differential equations, Rat. Mat. 1(1985), 267–274. Google Scholar

[9] 9. Grammatikopoulos, M. K., Ladas, G. and Meimaridou, A., Oscillation and asymptotic behaviour of second order neutral differential equations, Ann. Math. Pura Appl. 148(1987), 29–40. Google Scholar

[10] 10. Gyori, I. and Ladas, G., Oscillation Theory of Delay Differential Equations with Applications, Oxford Sci.Publ., Oxford, 1991. Google Scholar

[11] 11. Hale, J. K., Theory of Functional Differential Equations, Springer- Verlag, New York, 1977. Google Scholar

[12] 12. Hartman, P., On nonoscillatory linear differential equations of second order, Amer. J. Math. 74(1952), 389–400. Google Scholar

[13] 13. Kamenev, I. V., Integral criterion for oscillation of linear differential equations of second order, Mat. Zametki. (1978), 249-151. Google Scholar

[14] 14. Lalli, B. S., Ruan, S. and Zhang, B. S., Oscillation theorems for nth-order neutral functional differential equations, Ann. Differential Equations 8(1992), 401-413. Google Scholar

[15] 15. Leighton, W., The detection of the oscillation of solutions of a second order linear differential equation, Duke Math. J. 17(1950), 57–61. Google Scholar

[16] 16. Philos, Ch. G., Oscillation theorems for linear differential equations of second order, Arch. Math. 53(1989), 482–492. Google Scholar

[17] 17. Ruan, S., Oscillations of nth-order functional differential equations, Comput. Math, with Appl. (2-3) 21(1991), 95–102. Google Scholar

[18] 18. Travis, C. C., Oscillation theorems for second-order differential equations with functional arguments, Proc. Amer. Math. Soc. 31(1972), 199–202. Google Scholar

[19] 19. Waltman, P., A note on an oscillation criterion for an equation with afunctional argument, Canad. Math. Bull. 11(1968), 593–595. Google Scholar

[20] 20. Wintner, A., A criterion of oscillatory stability, Qurt. Appl. Math. 7(1949), 115–117. Google Scholar

[21] 21. Wong, J. S. W., An oscillation criterion for second order nonlinear differential equations with iterated integral averages, Differential Integral Equations 6(1993), 83–91. Google Scholar

[22] 22. Yan, J., Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc. 98(1986), 276–282. Google Scholar

Cité par Sources :