The Stability of Solutions of Generalized Emden-Fowler Equations
Canadian mathematical bulletin, Tome 17 (1974) no. 3, pp. 397-401

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

This paper gives several monotonicity properties of all oscillatory solutions of equations with separable and nonseparable nonlinearities which are more general than the Emden- Fowler equations * Principally, if x(t) is an oscillatory solution, conditions are given such that; if a(t)↑ ∞ as t → ∞, then x(t) → 0; and, if a(t) ↓ 0 as t → ∞, then lim sup | x(t) | = ∞.
DOI : 10.4153/CMB-1974-073-x
Mots-clés : 34C10, 34D99, Emden-Fowler equation, oscillation, monotonicity, stability, convexity
The Stability of Solutions of Generalized Emden-Fowler Equations. Canadian mathematical bulletin, Tome 17 (1974) no. 3, pp. 397-401. doi: 10.4153/CMB-1974-073-x
@misc{10_4153_CMB_1974_073_x,
     title = {The {Stability} of {Solutions} of {Generalized} {Emden-Fowler} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {397--401},
     year = {1974},
     volume = {17},
     number = {3},
     doi = {10.4153/CMB-1974-073-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-073-x/}
}
TY  - JOUR
TI  - The Stability of Solutions of Generalized Emden-Fowler Equations
JO  - Canadian mathematical bulletin
PY  - 1974
SP  - 397
EP  - 401
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-073-x/
DO  - 10.4153/CMB-1974-073-x
ID  - 10_4153_CMB_1974_073_x
ER  - 
%0 Journal Article
%T The Stability of Solutions of Generalized Emden-Fowler Equations
%J Canadian mathematical bulletin
%D 1974
%P 397-401
%V 17
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1974-073-x/
%R 10.4153/CMB-1974-073-x
%F 10_4153_CMB_1974_073_x

[1] 1. Burton, T. and Grimmer, R., On the asymptotic behavior of solutions of x″ + a(t)f(x)=0, Proc. Camb. Phil. Soc. 70 (1971), 77-88. Google Scholar

[2] 2. Das, K., Comparison and monotonity theorems for second order non-linear differential equations, Acta. Math. Sci. Hungar. 15 (1964), 449-456. Google Scholar

[3] 3. DeKleine, H. A., A counterexample to a conjecture in second-order linear equations, Mich. Math. J. 17 (1970), 29-32. Google Scholar

[4] 4. Hartman, P., The existence of large or small solutions of linear differential equations, Duke Math. J. 28 (1961), 421-430. Google Scholar

[5] 5. Heidel, J. W. and Hinton, D. B., The existence of oscillatory solutions for a nonlinear differential equation (to appear). Google Scholar

[6] 6. Hinton, D. B., Some stability conditions for a nonlinear differential equation, Trans. Amer. Math. Soc. 139 (1969), 349-358. Google Scholar

[7] 7. Chiou, Kuo-liang, A second order nonlinear oscillation theorem, SIAM J. Appl. Math. 21 (1971). Google Scholar

[8] 8. Wong, J. S. W., On the global asymptotic stability of(p(t)x/′)′+q(t)x2n-1=0 , J. Inst. Maths. Applies. 3 (1967), 403-05. Google Scholar

[9] 9. Wong, J. S. W., On second order nonlinear oscillation, Funkc. Ekvac. 11 (1969), 207-234. Google Scholar

Cité par Sources :