| Title:
|
Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems (English) |
| Author:
|
Kamo, Ken-ichi |
| Author:
|
Usami, Hiroyuki |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1153-1165 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider positive unbounded solutions of second order quasilinear ordinary differential equations. Our objective is to determine the asymptotic forms of unbounded solutions. An application to exterior Dirichlet problems is also given. (English) |
| Keyword:
|
quasilinear ordinary differential equation |
| Keyword:
|
asymptotic form |
| Keyword:
|
unbounded solution |
| MSC:
|
34C11 |
| MSC:
|
34D05 |
| MSC:
|
35B40 |
| MSC:
|
35D05 |
| MSC:
|
35D30 |
| MSC:
|
35J62 |
| idZBL:
|
Zbl 1174.34433 |
| idMR:
|
MR2471173 |
| . |
| Date available:
|
2010-07-21T08:13:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140447 |
| . |
| Reference:
|
[1] Bellman, R.: Stability Theory of Differential Equations.McGraw-Hill New York (1953) (Reprint: Dover, 1969). Zbl 0053.24705, MR 0061235 |
| Reference:
|
[2] Berkovich, L. M.: The generalized Emden-Fowler equation.In: Symmetry in Nonlinear Physics. Proc. 2nd International Conference, Kyiv, Ukraine, July 7-13, 1997 Institute of Mathematics of the National Academy of Sciences of Ukraine Kyiv (1997), 155-163. Zbl 0952.34030, MR 1600976 |
| Reference:
|
[3] Kamo, K.: Asymptotic equivalence for positive decaying solutions of quasilinear ordinary differential equations and its application to elliptic problems.Arch. Math., Brno 40 (2004), 209-217. MR 2068692 |
| Reference:
|
[4] Kamo, K., Usami, H.: Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equation.Adv. Math. Sci. Appl. 10 (2000), 673-688. MR 1807447 |
| Reference:
|
[5] Kamo, K., Usami, H.: Asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations with sub-homogeneity.Hiroshima Math. J. 31 (2001), 35-49. Zbl 0997.34038, MR 1820693, 10.32917/hmj/1151511146 |
| Reference:
|
[6] Kiguradze, I. T., Chanturiya, T. A.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Kluwer Dordrecht (1992). |
| Reference:
|
[7] Kura, T.: The weak supersolution-subsolution method for second order quasilinear elliptic equations.Hiroshima Math. J. 19 (1989), 1-36. Zbl 0735.35056, MR 1009660, 10.32917/hmj/1206129479 |
| Reference:
|
[8] Lima, P. M.: Numerical methods and asymptotic error expansions for the Emden-Fowler equations.J. Comput. Appl. Math. 70 (1996), 245-266. Zbl 0854.65067, MR 1399872, 10.1016/0377-0427(95)00203-0 |
| Reference:
|
[9] Luning, C. D., Perry, W. L.: Positive solutions of negative exponent generalized Emden-Fowler boundary value problems.SIAM J. Math. Anal. 12 (1981), 874-879. Zbl 0478.34021, MR 0635240, 10.1137/0512073 |
| Reference:
|
[10] Mizukami, M., Naito, M., Usami, H.: Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations.Hiroshima Math. J. 32 (2002), 51-78. Zbl 1017.34053, MR 1892669, 10.32917/hmj/1151007642 |
| Reference:
|
[11] Tanigawa, T.: Existence and asymptotic behavior of positive solutions of second order quasilinear differential equations.Adv. Math. Sci. Appl. 9 (1999), 907-938. Zbl 1025.34043, MR 1725693 |
| . |
