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Title: Asymptotic properties for half-linear difference equations (English)
Author: Cecchi, Mariella
Author: Došlá, Zuzana
Author: Marini, Mauro
Author: Vrkoč, Ivo
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 131
Issue: 4
Year: 2006
Pages: 347-363
Summary lang: English
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Category: math
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Summary: Asymptotic properties of the half-linear difference equation \[ \Delta (a_{n}|\Delta x_{n}|^{\alpha }\mathop {\mathrm sgn}\Delta x_{n} )=b_{n}|x_{n+1}|^{\alpha }\mathop {\mathrm sgn}x_{n+1} \qquad \mathrm{(*)}\] are investigated by means of some summation criteria. Recessive solutions and the Riccati difference equation associated to $(*)$ are considered too. Our approach is based on a classification of solutions of $(*)$ and on some summation inequalities for double series, which can be used also in other different contexts. (English)
Keyword: half-linear second order difference equation
Keyword: nonoscillatory solutions
Keyword: Riccati difference equation
Keyword: summation inequalities
MSC: 39A10
MSC: 39A11
idZBL: Zbl 1110.39004
idMR: MR2273927
DOI: 10.21136/MB.2006.133970
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Date available: 2009-09-24T22:27:17Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/133970
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Reference: [1] R. P. Agarwal: Difference Equations and Inequalities.2nd Edition, Pure Appl. Math. 228, Marcel Dekker, New York, 2000. Zbl 0952.39001, MR 1740241
Reference: [2] M. Cecchi, Z. Došlá, M. Marini: Positive decreasing solutions of quasi-linear difference equations.Comput. Math. Appl. 42 (2001), 1401–1410. MR 1861536
Reference: [3] M. Cecchi, Z. Došlá, M. Marini: On recessive and dominant solutions for half-linear difference equations.J. Differ. Equ. Appl. 10 (2004), 797–808. MR 2074433
Reference: [4] M. Cecchi, Z. Došlá, M. Marini, I. Vrkoč: Summation inequalities and half-linear difference equations.J. Math. Anal. Appl. 302 (2005), 1–13. MR 2106543
Reference: [5] M. Cecchi, Z. Došlá, M. Marini, I. Vrkoč: Integral conditions for nonoscillation of second order nonlinear differential equations.Nonlinear Anal., T.M.A. 64 (2006), 1278–1289. MR 2200492, 10.1016/j.na.2005.06.035
Reference: [6] M. Cecchi, Z. Došlá, M. Marini, I. Vrkoč: Nonoscillatory solutions for Emden-Fowler type difference equations.Proc. Inf. Conf. Difference Equations. Special Functions and Applications. Munich, 2005.
Reference: [7] Z. Došlá, I. Vrkoč: On extension of the Fubini theorem and its application to the second order differential equations.Nonlinear Anal., T.M.A. 57 (2004), 531–548. MR 2062993
Reference: [8] O. Došlý: Half-Linear Differential Equations.Handbook of Differential Equations, Ordinary Differential Equations I., A. Cañada, P. Drábek, A. Fonda (eds.), Elsevier, Amsterdam, 2004. Zbl 1090.34027, MR 2166491
Reference: [9] O. Došlý, P. Řehák: Nonoscillation criteria for half-linear second order difference equations.Comput. Math. Appl. 42 (2001), 453–464. MR 1838006
Reference: [10] O. Došlý, P. Řehák: Recessive solution of half-linear second order difference equations.J. Differ. Equ. Appl. 9 (2003), 49–61. MR 1958302, 10.1080/10236100309487534
Reference: [11] J. W. Hooker, W. T. Patula: A second-order nonlinear difference equation: oscillation and asymptotic behavior.J. Math. Anal. Appl. 91 (1983), 9–29. MR 0688528, 10.1016/0022-247X(83)90088-4
Reference: [12] P. Řehák: Oscillatory properties of second order half-linear difference equations.Czechoslovak Math. J. 51 (2001), 303–321. Zbl 0982.39004, MR 1844312, 10.1023/A:1013790713905
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