Oscillation Criteria for Second Order Nonlinear Delay Equations
Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 49-56

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

It is the purpose of this paper to establish oscillation criteria for second order nonlinear differential equations with retarded argument. Specifically, we consider the equation 1.1 where f ∊ C[0, + ∞) x R 2, g ∊ C[0, + ∞), and 1.2 We shall restrict attention to solutions of (1.1) which exist on some ray [T, + ∞). A solution of (1.1) is called oscillatory if it has no largest zero.
Erbe, Lynn. Oscillation Criteria for Second Order Nonlinear Delay Equations. Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 49-56. doi: 10.4153/CMB-1973-011-1
@article{10_4153_CMB_1973_011_1,
     author = {Erbe, Lynn},
     title = {Oscillation {Criteria} for {Second} {Order} {Nonlinear} {Delay} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {49--56},
     year = {1973},
     volume = {16},
     number = {1},
     doi = {10.4153/CMB-1973-011-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-011-1/}
}
TY  - JOUR
AU  - Erbe, Lynn
TI  - Oscillation Criteria for Second Order Nonlinear Delay Equations
JO  - Canadian mathematical bulletin
PY  - 1973
SP  - 49
EP  - 56
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-011-1/
DO  - 10.4153/CMB-1973-011-1
ID  - 10_4153_CMB_1973_011_1
ER  - 
%0 Journal Article
%A Erbe, Lynn
%T Oscillation Criteria for Second Order Nonlinear Delay Equations
%J Canadian mathematical bulletin
%D 1973
%P 49-56
%V 16
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1973-011-1/
%R 10.4153/CMB-1973-011-1
%F 10_4153_CMB_1973_011_1

[1] 1. El’gol’ts, L.E., Introduction to the theory of differential equations with deviating arguments, Holden-Day, San Francisco, Calif., 1966. Google Scholar

[2] 2. Gollwitzer, H.E., On nonlinear oscillations for a second order delay equation, J. Math. Anal. Appl. 26 (1969), 385–389. Google Scholar

[3] 3. Bradley, J.S., Oscillation theorems for a second order delay equation, J. Differential Equations, 8 (1970), 397–403. Google Scholar

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

[5] 5. Staikos, V.A. and Petsoulas, A.G., Some oscillation criteria for second order nonlinear delaydifferential equations, J. Math. Anal. Appl. 30 (1970), 695–701. Google Scholar

[6] 6. Ladas, G., Oscillation and asymptotic behavior of solutions of differential equations with retarded argument, Technical Report No. 10, Mathematics Department, Univ. of Rhode Island, July 1970. Google Scholar

[7] 7. Atkinson, F.V., On second order nonlinear oscillations. Pacific J. Math. 5 (1955), 643–647. Google Scholar

[8] 8. Wong, J.S.W., On second order nonlinear oscillation. Funkcial. Ekvac. 11 (1968), 207–234. Google Scholar

[9] 9. Hartman, P., Ordinary differential equations, Wiley, New York, 1964. Google Scholar

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

[11] 11. Hille, E., Nonoscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234–252. Google Scholar

[12] 12. Jackson, L.K., Sub functions and second order differential inequalities, Advances in Math. 2 (1968), 307–363. Google Scholar

[13] 13. Belohorec, S., Oscillatory solutions of certain nonlinear differential equations of the second order, (Czech), Mat.-Fyz. Časopis Sloven. Akad. Vied. (4) 11 (1961), 250–255. Google Scholar

[14] 14. Jones, J. Jr On the extension of a theorem of Atkinson, Quart. J. Math. Oxford Ser. 7 (1956), 306–309. Google Scholar

Cité par Sources :