Geodesic
Asymptotic Behaviour of Nonoscillatory Equations
Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 436-453

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

For nonlinear equations of the form I there has been considerable interest in determining the asymptotic forms of nonoscillatory solutions. We assume r(t) is continuous and positive on [0, ∞), and f(t, x) is continuous on [0, ∞) × R, and f(t, x) ≥ 0 for x ≠ 0. For n = 2, equation (I) was studied by Kusano and Naito [3], who found necessary and sufficient conditions for the existence of minimal and maximal nonoscillatory solutions. The former are the bounded solutions, while the later are those asymptotic to the function 1.1 Their method consisted of writing (I) in the form of an integral operator and applying the Schauder fixed point theorem. For arbitrary n, but for r(t) = 1, Kreith [2] found necessary and sufficient conditions for the existence of maximal solutions. 
Edelson, Allan L.; Perri, Emilia. Asymptotic Behaviour of Nonoscillatory Equations. Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 436-453. doi: 10.4153/CJM-1983-024-2
@article{10_4153_CJM_1983_024_2,
     author = {Edelson, Allan L. and Perri, Emilia},
     title = {Asymptotic {Behaviour} of {Nonoscillatory} {Equations}},
     journal = {Canadian journal of mathematics},
     pages = {436--453},
     year = {1983},
     volume = {35},
     number = {3},
     doi = {10.4153/CJM-1983-024-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-024-2/}
}
TY  - JOUR
AU  - Edelson, Allan L.
AU  - Perri, Emilia
TI  - Asymptotic Behaviour of Nonoscillatory Equations
JO  - Canadian journal of mathematics
PY  - 1983
SP  - 436
EP  - 453
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-024-2/
DO  - 10.4153/CJM-1983-024-2
ID  - 10_4153_CJM_1983_024_2
ER  - 
%0 Journal Article
%A Edelson, Allan L.
%A Perri, Emilia
%T Asymptotic Behaviour of Nonoscillatory Equations
%J Canadian journal of mathematics
%D 1983
%P 436-453
%V 35
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-024-2/
%R 10.4153/CJM-1983-024-2
%F 10_4153_CJM_1983_024_2

[1] 1. Edelson, A. L. and Schuur, J., Asymptotic behaviour of nth order equations, Pacific J. Math, (to appear). Google Scholar

[2] 2. Kreith, K., Extremal solutions for a class of nonlinear differential equations, Proc. Amer. Math. Soc. 79 (1980), 415–421. Google Scholar

[3] 3. Kusano, T. and Naito, M., Nonlinear oscillation of fourth order differential equations, Can. J. Math. 28 (1976), 840–852. Google Scholar

Cité par Sources :