Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations

Ethiraju Thandapani; L. Ramuppillai

Archivum Mathematicum (1998)

  • Volume: 034, Issue: 4, page 455-466
  • ISSN: 0044-8753

Abstract

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This paper deals with oscillatory and asymptotic behaviour of solutions of second order quasilinear difference equation of the form Δ ( a n - 1 | Δ y n - 1 | α - 1 Δ y n - 1 ) + F ( n , y n ) = G ( n , y n , Δ y n ) , n ∈ N ( n 0 ) ( E ) where α > 0 . Some sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) are also considered.

How to cite

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Thandapani, Ethiraju, and Ramuppillai, L.. "Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations." Archivum Mathematicum 034.4 (1998): 455-466. <http://eudml.org/doc/248211>.

@article{Thandapani1998,
abstract = {This paper deals with oscillatory and asymptotic behaviour of solutions of second order quasilinear difference equation of the form \[ \Delta (a\_\{n-1\}| \Delta y\_\{n-1\}|^\{\alpha -1\} \Delta y\_\{n-1\})+ F(n, y\_n)= G(n, y\_n, \Delta y\_n), \quad n\in N(n\_0) \qquad \mathrm \{(E)\}\] where $\alpha >0$. Some sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) are also considered.},
author = {Thandapani, Ethiraju, Ramuppillai, L.},
journal = {Archivum Mathematicum},
keywords = {perturbed quasilinear difference equation; oscillatory solution; perturbed quasilinear difference equation; oscillatory solution; asymptotic; nonoscillatory solutions; -function technique; oscillation},
language = {eng},
number = {4},
pages = {455-466},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations},
url = {http://eudml.org/doc/248211},
volume = {034},
year = {1998},
}

TY - JOUR
AU - Thandapani, Ethiraju
AU - Ramuppillai, L.
TI - Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations
JO - Archivum Mathematicum
PY - 1998
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 034
IS - 4
SP - 455
EP - 466
AB - This paper deals with oscillatory and asymptotic behaviour of solutions of second order quasilinear difference equation of the form \[ \Delta (a_{n-1}| \Delta y_{n-1}|^{\alpha -1} \Delta y_{n-1})+ F(n, y_n)= G(n, y_n, \Delta y_n), \quad n\in N(n_0) \qquad \mathrm {(E)}\] where $\alpha >0$. Some sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) are also considered.
LA - eng
KW - perturbed quasilinear difference equation; oscillatory solution; perturbed quasilinear difference equation; oscillatory solution; asymptotic; nonoscillatory solutions; -function technique; oscillation
UR - http://eudml.org/doc/248211
ER -

References

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  11. Asymptotic behaviour of solutions of Emden-Fowler difference equations with oscillating coefficients, J. Math. Anal. Appl. 179(1993), 135-153. MR1244954
  12. Oscillation theorems and existence of positive monotone solutions for second order nonlinear difference equations, Math. Comput. Modelling 21(1995), 63-84. MR1316120
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