On asymptotic behavior of solutions of n -th order Emden-Fowler differential equations with advanced argument

Roman Koplatadze

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 3, page 817-833
  • ISSN: 0011-4642

Abstract

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We study oscillatory properties of solutions of the Emden-Fowler type differential equation u ( n ) ( t ) + p ( t ) | u ( σ ( t ) ) | λ sign u ( σ ( t ) ) = 0 , where 0 < λ < 1 , p ∈ L loc ( ℝ + ; ℝ ) , σ ∈ C ( ℝ + ; ℝ + ) and σ ( t ) ≥ t for t ∈ ℝ + . Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).

How to cite

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Koplatadze, Roman. "On asymptotic behavior of solutions of $n$-th order Emden-Fowler differential equations with advanced argument." Czechoslovak Mathematical Journal 60.3 (2010): 817-833. <http://eudml.org/doc/38043>.

@article{Koplatadze2010,
abstract = {We study oscillatory properties of solutions of the Emden-Fowler type differential equation \[u^\{(n)\}(t)+p(t)\big |u(\sigma (t))\big |^\lambda \operatorname\{sign\} u(\sigma (t))=0,\] where $0<\lambda <1$, $p\in L_\{\rm loc \}(\mathbb \{R\}_+;\mathbb \{R\})$, $\sigma \in C(\mathbb \{R\}_+;\mathbb \{R\}_+)$ and $\sigma (t)\ge t$ for $t\in \mathbb \{R\}_+$. Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).},
author = {Koplatadze, Roman},
journal = {Czechoslovak Mathematical Journal},
keywords = {proper solution; property A; property B ; proper solution; property , property },
language = {eng},
number = {3},
pages = {817-833},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On asymptotic behavior of solutions of $n$-th order Emden-Fowler differential equations with advanced argument},
url = {http://eudml.org/doc/38043},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Koplatadze, Roman
TI - On asymptotic behavior of solutions of $n$-th order Emden-Fowler differential equations with advanced argument
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 817
EP - 833
AB - We study oscillatory properties of solutions of the Emden-Fowler type differential equation \[u^{(n)}(t)+p(t)\big |u(\sigma (t))\big |^\lambda \operatorname{sign} u(\sigma (t))=0,\] where $0<\lambda <1$, $p\in L_{\rm loc }(\mathbb {R}_+;\mathbb {R})$, $\sigma \in C(\mathbb {R}_+;\mathbb {R}_+)$ and $\sigma (t)\ge t$ for $t\in \mathbb {R}_+$. Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).
LA - eng
KW - proper solution; property A; property B ; proper solution; property , property
UR - http://eudml.org/doc/38043
ER -

References

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  1. Kiguradze, I., Stavroulakis, I., 10.1080/00036819808840679, Appl. Anal. 70 (1998), 97-112. (1998) Zbl1013.34068MR1671550DOI10.1080/00036819808840679
  2. Kondrat'ev, V. A., Oscillatory properties of solutions of the equation y ( n ) + p ( x ) y = 0 , Russian Trudy Moskov. Mat. Obsc. 10 (1961), 419-436. (1961) MR0141842
  3. Koplatadze, R., 10.1016/0022-247X(73)90127-3, J. Math. Anal. Appl. 42 (1973), 148-157. (1973) Zbl0255.34069MR0322313DOI10.1016/0022-247X(73)90127-3
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  5. Koplatadze, R., Chanturia, T., Oscillatory properties of differential equations with deviating argument, Russian With Georgian and English summaries. Izdat. Tbilis. Univ., Tbilisi (1977), 115. (1977) MR0492725
  6. Koplatadze, R., Some properties of the solutions of nonlinear differential inequalities and equations with retarded argument, Russian Differentsial'nye Uravneniya 12 (1976), 1971-1984. (1976) MR0466843
  7. Koplatadze, R., On oscillatory properties of solutions of functional-differential equations, Mem. Differential Equations Math. Phys. 3 (1994), 179 pp. (1994) Zbl0843.34070MR1375838
  8. Koplatadze, R., On asymptotic behaviour of solutions of functional-differential equations, Equadiff 8 (Bratislava, 1993). Tatra Mt. Math. Publ. 4 (1994), 143-146. (1994) Zbl0809.34081MR1298463
  9. Koplatadze, R., 10.1016/j.jmaa.2006.07.085, J. Math. Anal. Appl. 330 (2007), 483-510. (2007) MR2302938DOI10.1016/j.jmaa.2006.07.085
  10. Graef, J., Koplatadze, R., Kvinikadze, G., 10.1016/j.jmaa.2004.12.034, J. Math. Anal. Appl. 306 (2005), 136-160. (2005) Zbl1069.34088MR2132894DOI10.1016/j.jmaa.2004.12.034
  11. Koplatadze, R., On asymptotic behavior of solutions of Emden-Fowler advanced differential equation, Math. Modeling and Computer Simulation of Material Technologies. Proceedings of the 5-th International Conference Ariel 2 (2008), 731-735. (2008) 
  12. Koplatadze, R., On oscillatory properties of solutions of generalized Emden-Fowler type differential equations, Proc. A. Razmadze Math. Inst. 145 (2007), 117-121. (2007) Zbl1154.34323MR2387454
  13. Koplatadze, R., On asymptotic behavior of solutions of almost linear and essentially nonlinear differential equations, Nonlinear Anal. Theory, Methods and Appl. (accepted). 
  14. Gramatikopoulos, M. K., Koplatadze, R., Kvinikadze, G., 10.1016/S0022-247X(03)00356-1, J. Math. Anal. Appl. 284 (2003), 294-314. (2003) MR1996134DOI10.1016/S0022-247X(03)00356-1

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