# 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

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topThandapani, 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

top- Difference Equations and Inequalities, Marcel Dekker, New York, 1992. Zbl0952.39001MR1155840
- Oscillatory and asymptotic behaviour of second order nonlinear difference equations, Proc. Edin. Math. Soc. 39(1996), 525-533. MR1417694
- Positive solutions of second order nonlinear difference equation, J. Math. Anal. Appl. 204(1996), 482-493. MR1421461
- Bounded and zero convergent solutions of second order difference equations, J. Math. Anal. Appl. 14(1989), 141-149. MR1009057
- Inequalities, 2nd Edition, Cambridge University Press, 1988. MR0944909
- Oscillatory and asymptotic behaviour of second order nonlinear difference equations, J. Math. Anal. Appl. 175(1993), 482-498. Zbl0780.39001MR1219191
- Nonoscillation, oscillation and growth of solutions of nonlinear difference equations of second order, J. Math. Anal. Appl. 109(1985), 22-30. Zbl0589.39003MR0796040
- Oscillation theorems for perturbed nonlinear second order difference equations, Computers Math. Appl. 28(1994), 309-316. Zbl0807.39002MR1284245
- Oscillation and nonoscillation theorems for a class of second order quasilinear difference equations, ZAA, 16 (1997), 749-759. MR1472729
- Oscillation theory for a class of second order quasilinear difference equations, Tamkang J. Math.Tamkang J. Math. 28 (1997), 229-238. MR1486791
- Asymptotic behaviour of solutions of Emden-Fowler difference equations with oscillating coefficients, J. Math. Anal. Appl. 179(1993), 135-153. MR1244954
- Oscillation theorems and existence of positive monotone solutions for second order nonlinear difference equations, Math. Comput. Modelling 21(1995), 63-84. MR1316120
- Oscillation and monotone solutions of second order quasilinear difference equations, Funk. Ekva. 39(1996), 491-517. MR1433914
- Higher type oscillation criterion and Sturm type comparison theorem, Math. Nachr. 153(1991), 485-496. MR1131938

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