Geodesic
Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation
Kybernetika, Tome 35 (1999) no. 4, pp. 499-506 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form $\Delta ^2y_{n-1}+q_ny_{\sigma (n)}^\gamma =g_n$, where $\gamma $ is a quotient of odd positive integers, in the superlinear case $(\gamma >1)$ and in the sublinear case $(\gamma 1)$.
In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form $\Delta ^2y_{n-1}+q_ny_{\sigma (n)}^\gamma =g_n$, where $\gamma $ is a quotient of odd positive integers, in the superlinear case $(\gamma >1)$ and in the sublinear case $(\gamma 1)$.
Classification : 34K40, 39A05, 39A10, 39A12, 39A21
Keywords: oscillation; nonlinear delay difference equation; Emden-Fowler type 
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     title = {Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation},
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Thandapani, E.; Ramuppillai, L. Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation. Kybernetika, Tome 35 (1999) no. 4, pp. 499-506. http://geodesic.mathdoc.fr/item/KYB_1999_35_4_a7/

[1] Agarwal R. P.: Difference Equations and Inequalities. Marcel Dekker, New York 1992 | MR | Zbl

[2] Gaef J. R., Spikes P. W.: Boundedness and asymptotic behavior of solutions of a forced difference equation. Internat. J. Math. Math. Sci. 17 (1994), 397–400 | DOI | MR

[3] Gaef J. R., Spikes P. W.: Asymptotic decay of oscillatory solutions of forced nonlinear difference equations. Dynamic Systems Appl. 3 (1994), 95–102 | MR

[4] Hooker J. W.: Some differences between difference equations and differential equations. J. Differential Equations Appl. 2 (1996), 219–226 | DOI | MR | Zbl

[5] Hooker J. W., Patula W. T.: A second order nonlinear difference equation: oscillation and asymptotic behavior. J. Math. Anal. Appl. 91 (1983), 9–29 | DOI | MR | Zbl

[6] Kordonis I. G. E., Philos, Ch. G., Purnaras I. K.: On the oscillation of some linear difference equations with periodic coefficients. J. Comput. Appl. Math. 84 (1997), 219–241 | DOI | MR | Zbl

[7] Lakshmikantham V., Trigiante D.: Theory of Difference Equations: Numerical Methods and Applications. Academic Press, New York 1988 | MR | Zbl

[8] Moore R. E.: Computational Functional Analysis. (Ellis Harwood Series.) Halstred Press, New York 1985 | MR | Zbl

[9] Patula W. T.: Growth, oscillation and comparison theorems for second order linear difference equation. SIAM J. Math. Anal. 10 (1979), 1272–1279 | DOI | MR

[10] Popenda J.: On the oscillation of solutions of difference equations. Demonstratio Math. 28 (1995), 575–586 | MR | Zbl

[11] Szmanda B.: Nonoscillation, oscillation and growth of solutions of nonlinear difference equations of second order. J. Math. Anal. Appl. 109 (1985), 22–30 | DOI | MR | Zbl

[12] Thandapani E., Pandian S.: On the oscillatory behavior of solutions of second order nonlinear difference equation. Z. Anal. Anwendungen 13 (1993), 347–358

[13] Thandapani E., Ramuppillai L.: Oscillation theorems for certain class of nonlinear difference equations. Z. Anal. Anwendungen 17 (1998), 1–10 | DOI | MR | Zbl

[14] Zafer A.: On the existence of positive solutions and oscillation of solutions of higher order differenced equations with forcing terms. Comput. Math. Appl., to appear | MR

[15] Zhang B. G.: Oscillation and asymptotic behavior of second order difference equations. J. Math. Anal. Appl. 173 (1993), 58–68 | DOI | MR | Zbl