Geodesic
Nonoscillation of Second Order Superlinear Differential Equations
Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 178-186

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

Some sufficient conditions are given for all solutions of the nonlinear differential equation y′′(x) +p(x)f(y) = 0 to be nonoscillatory, where p is positive and for a quotient γ of odd positive integers, γ > 1.
DOI : 10.4153/CMB-1994-027-6
Mots-clés : 34C15 
Erbe, L. H.; Xia, H. X.; Wu, J. H. Nonoscillation of Second Order Superlinear Differential Equations. Canadian mathematical bulletin, Tome 37 (1994) no. 2, pp. 178-186. doi: 10.4153/CMB-1994-027-6
@article{10_4153_CMB_1994_027_6,
     author = {Erbe, L. H. and Xia, H. X. and Wu, J. H.},
     title = {Nonoscillation of {Second} {Order} {Superlinear} {Differential} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {178--186},
     year = {1994},
     volume = {37},
     number = {2},
     doi = {10.4153/CMB-1994-027-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-027-6/}
}
TY  - JOUR
AU  - Erbe, L. H.
AU  - Xia, H. X.
AU  - Wu, J. H.
TI  - Nonoscillation of Second Order Superlinear Differential Equations
JO  - Canadian mathematical bulletin
PY  - 1994
SP  - 178
EP  - 186
VL  - 37
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-027-6/
DO  - 10.4153/CMB-1994-027-6
ID  - 10_4153_CMB_1994_027_6
ER  - 
%0 Journal Article
%A Erbe, L. H.
%A Xia, H. X.
%A Wu, J. H.
%T Nonoscillation of Second Order Superlinear Differential Equations
%J Canadian mathematical bulletin
%D 1994
%P 178-186
%V 37
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-027-6/
%R 10.4153/CMB-1994-027-6
%F 10_4153_CMB_1994_027_6

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

[2] 2. Belohorec, S., Oscillatory solutions of certain nonlinear differential equations of second order, Mat. Casopis Sloven, Akad. Vied. 11(1961), 250–255. Google Scholar

[3] 3. Belohorec, S., On some properties of the equation y″(x)+f(x)yα(x) = 0, 0 < α <1, Mat. Casopis Solven. Akad. Vied. 17(1967), 10–19. Google Scholar

[4] 4. Chiou, K. L., The existence of oscillatory solutions for the equation Proc. Amer. Math. Soc. 35(1972), 120–122. Google Scholar

[5] 5. Chiou, K. L., A nonoscillation theorem for the superlinear case of second order differential equations y″ + yF(y2,x) =0, SIAM J. Appl. Math. 23(1972), 456–459. Google Scholar

[6] 6. 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

[7] 7. Coffman, C. V. and Wong, J. S. W., Oscillation and nonoscillation theorems for the generalized Emden-Fowler equations, Trans. Amer. Math. Soc. 167(1973), 399–434. Google Scholar

[8] 8. Erbe, L. H., Nonoscillation criteria for second order nonlinear differential equations, J. Math. Anal. Appl. 108(1985), 515–527. Google Scholar

[9] 9. Erbe, L. H., Oscillation and nonoscillationpropertiesfor second order nonlinear differential equations, Equadiff 82, Wurzburg, 1982. Lecture Notes in Math., Springer, 1983, 168–176. Google Scholar

[10] 10. Erbe, L. H. and Hong Lu, Nonoscillation theorems for second order nonlinear differential equations, Funkcial. Ekvac. 33(1990), 227–244. Google Scholar

[11] 11. Erbe, L. H. and Muldowney, J. S., On the existence of oscillatory solutions to nonlinear differential equations, Ann. Math. Pura. Appl. 59(1976), 23–37. Google Scholar

[12] 12. Erbe, L. H. and Muldowney, J. S., Nonoscillation results for second order nonlinear differential equations, Rocky Mountain J. Math. 12(1982), 635–642. Google Scholar

[13] 13. Fowler, R. H., Further studies of Emden 's and similar differential equations, Quart. J. Math. 2(1931 ), 259– 288. Google Scholar

[14] 14. Gidas, B., Ni, W. M. and Nirenberg, L., Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68(1979), 209–243. Google Scholar

[15] 15. Kaper, H. G. and Kwong, M. K., A non-oscillation theorem for the Emden-Fowler equation: ground states for semilinear elliptic equations with critical exponents, J. Differential Equations 75(1988), 158–185. Google Scholar

[16] 16. Nehari, Z., A nonlinear oscillation theorem, Duke Math. J. 42(1975), 183–189. 17 , Mathematical Reviews, (11661), 48, (1974). Google Scholar

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

[19] 19. Wong, J. S. W., Oscillation theorems for second order nonlinear differential equations, Bull. Inst. Math. Acad. Sinica 3(1975), 283–309. Google Scholar

[20] 20. Wong, J. S. W., On the generalized Emden-Fowler equation, SIAM Rev. 17(1975), 339–360. Google Scholar

Cité par Sources :