Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems

Ken-ichi Kamo; Hiroyuki Usami

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 4, page 1153-1165
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Kamo, Ken-ichi, and Usami, Hiroyuki. "Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems." Czechoslovak Mathematical Journal 58.4 (2008): 1153-1165. <http://eudml.org/doc/37893>.

@article{Kamo2008,
abstract = {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.},
author = {Kamo, Ken-ichi, Usami, Hiroyuki},
journal = {Czechoslovak Mathematical Journal},
keywords = {quasilinear ordinary differential equation; asymptotic form; unbounded solution; quasilinear ordinary differential equation; asymptotic form; unbounded solution},
language = {eng},
number = {4},
pages = {1153-1165},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems},
url = {http://eudml.org/doc/37893},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Kamo, Ken-ichi
AU - Usami, Hiroyuki
TI - Positive unbounded solutions of second order quasilinear ordinary differential equations and their application to elliptic problems
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 1153
EP - 1165
AB - 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.
LA - eng
KW - quasilinear ordinary differential equation; asymptotic form; unbounded solution; quasilinear ordinary differential equation; asymptotic form; unbounded solution
UR - http://eudml.org/doc/37893
ER -

References

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  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. (1997) Zbl0952.34030MR1600976
  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. (2004) MR2068692
  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. (2000) MR1807447
  5. Kamo, K., Usami, H., 10.32917/hmj/1151511146, Hiroshima Math. J. 31 (2001), 35-49. (2001) Zbl0997.34038MR1820693DOI10.32917/hmj/1151511146
  6. Kiguradze, I. T., Chanturiya, T. A., Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Kluwer Dordrecht (1992). (1992) 
  7. Kura, T., 10.32917/hmj/1206129479, Hiroshima Math. J. 19 (1989), 1-36. (1989) Zbl0735.35056MR1009660DOI10.32917/hmj/1206129479
  8. Lima, P. M., 10.1016/0377-0427(95)00203-0, J. Comput. Appl. Math. 70 (1996), 245-266. (1996) Zbl0854.65067MR1399872DOI10.1016/0377-0427(95)00203-0
  9. Luning, C. D., Perry, W. L., 10.1137/0512073, SIAM J. Math. Anal. 12 (1981), 874-879. (1981) Zbl0478.34021MR0635240DOI10.1137/0512073
  10. Mizukami, M., Naito, M., Usami, H., 10.32917/hmj/1151007642, Hiroshima Math. J. 32 (2002), 51-78. (2002) Zbl1017.34053MR1892669DOI10.32917/hmj/1151007642
  11. Tanigawa, T., Existence and asymptotic behavior of positive solutions of second order quasilinear differential equations, Adv. Math. Sci. Appl. 9 (1999), 907-938. (1999) Zbl1025.34043MR1725693

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