Geodesic
Uniform estimates for positive solutions of quasi-linear ordinary differential equations
Izvestiya. Mathematics , Tome 72 (2008) no. 6, pp. 1141-1160.

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain uniform estimates for positive solutions of higher-order quasi-linear differential equations that have a common domain and depend on estimates for the coefficients of the equation but not on the coefficients themselves.
Keywords: quasi-linear differential equation
Mots-clés : positive solutions. 
@article{IM2_2008_72_6_a3,
     author = {I. V. Astashova},
     title = {Uniform estimates for positive solutions of quasi-linear ordinary differential equations},
     journal = {Izvestiya. Mathematics },
     pages = {1141--1160},
     publisher = {mathdoc},
     volume = {72},
     number = {6},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_6_a3/}
}
TY  - JOUR
AU  - I. V. Astashova
TI  - Uniform estimates for positive solutions of quasi-linear ordinary differential equations
JO  - Izvestiya. Mathematics 
PY  - 2008
SP  - 1141
EP  - 1160
VL  - 72
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2008_72_6_a3/
LA  - en
ID  - IM2_2008_72_6_a3
ER  - 
%0 Journal Article
%A I. V. Astashova
%T Uniform estimates for positive solutions of quasi-linear ordinary differential equations
%J Izvestiya. Mathematics 
%D 2008
%P 1141-1160
%V 72
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2008_72_6_a3/
%G en
%F IM2_2008_72_6_a3
I. V. Astashova. Uniform estimates for positive solutions of quasi-linear ordinary differential equations. Izvestiya. Mathematics , Tome 72 (2008) no. 6, pp. 1141-1160. http://geodesic.mathdoc.fr/item/IM2_2008_72_6_a3/

[1] I. T. Kiguradze, T. A. Chanturia, Asymptotic properties of solutions of nonautonomous ordinary differential equations, Math. Appl. (Soviet Ser.), 89, Kluwer, Dordrecht, 1993 | MR | Zbl | Zbl

[2] I. V. Astashova, “Application of dynamical systems to the study of asymptotic properties of solutions to nonlinear higher-order differential equations”, J. Math. Sci. (N. Y.), 126:5 (2005), 1361–1391 | DOI | MR | Zbl

[3] T. A. Chanturiya, “Existence of singular and unbounded oscillating solutions of differential equations of Emden–Fowler type”, Differential Equations, 28:6 (1992), 811–824 | MR | Zbl

[4] V. A. Kozlov, “On Kneser solutions of higher order nonlinear ordinary differential equations”, Ark. Mat., 37:2 (1999), 305–322 | DOI | MR | Zbl

[5] G. G. Kvinikadze, I. T. Kiguradze, “O bystro rastuschikh resheniyakh nelineinykh obyknovennykh differentsialnykh uravnenii”, Soobsch. AN GSSR, 106:3 (1982), 465–468 | MR | Zbl

[6] V. A. Kondrat'ev, “On qualitative properties of the solutions of semilinear elliptic equations”, J. Math. Sci., 69:3 (1994), 1068–1071 | DOI | MR | Zbl

[7] O. A. Oleinik, “Joint sessions of the Petrovskii Seminar on differential equations and related problems and the Moscow Mathematical Society”, Russian Math. Surveys, 51:5 (1996), 911–998 | DOI

[8] I. V. Astashova, “Estimates of solutions to one-dimensional Schrödinger equation”, Progress in analysis, vol. II (Berlin, 2001), World Sci. Publ., River Edge, NJ, 2003, 955–960 | MR | Zbl

[9] G. Pólya, “On the mean-value theorem corresponding to a given linear homogeneous differential equation”, Trans. Amer. Math. Soc., 24:4 (1922), 312–324 | DOI | MR | Zbl

[10] J. de la Vallée-Poussin, “Sur l'équation différentielle linéaire du second ordre. Détermination d'une intégrale par deux valeurs assignées. Extension aux équations d'ordre $n$”, Journ. de Math., 9:8 (1929), 125–144 | Zbl

[11] A. Yu. Levin, “Non-oscillation of solutions of the equation $x^{(n)}+p_1(t)x^{(n-1)}+\dots+p_n(t)x=0$”, Russian Math. Surveys, 24:2 (1969), 43–99 | DOI | MR | Zbl

[12] I. V. Astashova, “On uniform estimates of positive solutions of quasilinear differential equations”, On the seminar on qualitative theory of differential equations at Moscow State University, Differ. Equ., 41:11 (2005), 1656–1657 | DOI

[13] I. V. Astashova, “Uniform estimates for positive solutions to quasi-linear differential equations of even order”, J. Math. Sci. (N. Y.), 135:1 (2006), 2616–2624 | DOI | MR | Zbl

[14] E. Mitidieri, S. I. Pokhozhaev, “A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities”, Proc. Steklov Inst. Math., 234:3 (2001), 1–362 | MR | Zbl | Zbl

[15] J. Hay, “Necessary conditions for the existence of global solutions of higher-order nonlinear ordinary differential inequalities”, Differ. Equ., 38:3 (2002), 362–368 | DOI | MR | Zbl

[16] A. A. Kon'kov, “On solutions of non-autonomous ordinary differential equations”, Izv. Math., 65:2 (2001), 285–327 | DOI | MR | Zbl

[17] I. V. Astashova, “Uniform estimates for positive solutions of quasilinear differential equations”, Dokl. Math., 74:1 (2006), 555–558 | DOI | MR | Zbl