Oscillation Theorems for Nonlinear Ordinary Differential Equations of Even Order
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 409-413

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

Consider the differential equation 1 where n is even and f(t, y) is subject to the following conditions:(a) f(t, y) is continuous on [0, ∞)× R;(2) (b) f(t, y) is nondecreasing in y for each fixed t∈[0,∞);(c) yf(t, y ) > 0 for y ≠ 0 and t∈[0,∞).
Kreith, Kurt; Kusano, Takaŝi. Oscillation Theorems for Nonlinear Ordinary Differential Equations of Even Order. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 409-413. doi: 10.4153/CMB-1981-063-1
@article{10_4153_CMB_1981_063_1,
     author = {Kreith, Kurt and Kusano, Taka\^{s}i},
     title = {Oscillation {Theorems} for {Nonlinear} {Ordinary} {Differential} {Equations} of {Even} {Order}},
     journal = {Canadian mathematical bulletin},
     pages = {409--413},
     year = {1981},
     volume = {24},
     number = {4},
     doi = {10.4153/CMB-1981-063-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-063-1/}
}
TY  - JOUR
AU  - Kreith, Kurt
AU  - Kusano, Takaŝi
TI  - Oscillation Theorems for Nonlinear Ordinary Differential Equations of Even Order
JO  - Canadian mathematical bulletin
PY  - 1981
SP  - 409
EP  - 413
VL  - 24
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-063-1/
DO  - 10.4153/CMB-1981-063-1
ID  - 10_4153_CMB_1981_063_1
ER  - 
%0 Journal Article
%A Kreith, Kurt
%A Kusano, Takaŝi
%T Oscillation Theorems for Nonlinear Ordinary Differential Equations of Even Order
%J Canadian mathematical bulletin
%D 1981
%P 409-413
%V 24
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-063-1/
%R 10.4153/CMB-1981-063-1
%F 10_4153_CMB_1981_063_1

[1] 1. Atkinson, F. V., On second-order non-linear oscillations, Pacific J. Math. 5 (1955), 643-647. Google Scholar

[2] 2. Belohorec, Š., Oscilatorické riešenia istej nelinéarnej deferencíalnej rownice druhého rádu, Math. -Fyz. Časopis Sloven. Akad. Ved. 11 (1961), 250-255. Google Scholar

[3] 3. Burton, T. A., Non-continuation of solutions of differential equations of order N, Atti. Accad. Naz. Lincei Rend. LIX (1975), 706-711. Google Scholar

[4] 4. Coffman, C. V. and Wong, J. S. W., On a second order nonlinear oscillation problem, Trans. Amer. Math. Soc. 147 (1970), 357-366. Google Scholar

[5] 5. Coffman, C. V. and Wong, J. S. W., Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations, Trans. Amer. Math. Soc. 167 (1972), 399-434. Google Scholar

[6] 6. Izjumova, D. V., On the conditions of oscillation and non-oscillation of second order nonlinear differential equations, Differencial'nye Uravnenij. 2 (1966), 1572-1585. (Russian) Google Scholar

[7] 7. Kiguradze, I. T., On oscillation of solutions of some ordinary differential equations, Dokl. Akad. Nauk SSS. 144 (1962), 33-36. (Russian) Google Scholar

[8] 8. 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

[9] 9. Kiguradze, I. T., The problem of oscillation of solutions of nonlinear differential equations, Differencial'nye Uravnenij. 1 (1965), 995-1006. (Russian) Google Scholar

[10] 10. Kiguradze, I. T., Some Singular Boundary Value Problems for Ordinary Differential Equations, Tbilsi University Press (1975), Tbilsi. Google Scholar

[11] 11. Kusano, T. and Onose, H., Oscillation of solutions of nonlinear differential delay equations of arbitrary order, Hiroshima Math. J. 2 (1972), 1-13. Google Scholar

[12] 12. Ličko, I. and Švec, M., Le caractère oscillatoire des solutions de l'équation y(n)+f(x)yα =0, n > l, Czechoslovak Math. J. 13 (1963), 481-491. +l,+Czechoslovak+Math.+J.+13+(1963),+481-491.>Google Scholar

[13] 13. Macki, J. W. and Wong, J. S. W., Oscillation of solutions of second order nonlinear differential equations, Pacific J. Math. 24 (1968), 111-118. Google Scholar

[14] 14. Onose, H., Oscillation and asymptotic behavior of solutions of retarded differential equations of arbitrary order, Hiroshima Math. J. 3 (1973), 333-360. Google Scholar

[15] 15. Ryder, G. H. and Wend, D. V. V., Oscillation of solutions of certain ordinary differential equations of n-th order, Proc. Amer. Math. Soc. 25 (1970), 463-469. Google Scholar

Cité par Sources :