Title:
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Periodic solutions of second order nonlinear functional difference equations (English) |
Author:
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Liu, Yuji |
Language:
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English |
Journal:
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Archivum Mathematicum |
ISSN:
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0044-8753 (print) |
ISSN:
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1212-5059 (online) |
Volume:
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43 |
Issue:
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1 |
Year:
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2007 |
Pages:
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67-74 |
Summary lang:
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English |
. |
Category:
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math |
. |
Summary:
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Sufficient conditions for the existence of at least one $T-$periodic solution of second order nonlinear functional difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results. (English) |
Keyword:
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periodic solutions |
Keyword:
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second order functional difference equation |
Keyword:
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fixed-point theorem |
Keyword:
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growth condition |
MSC:
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39A11 |
MSC:
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47N20 |
idZBL:
|
Zbl 1164.39005 |
idMR:
|
MR2310126 |
. |
Date available:
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2008-06-06T22:50:35Z |
Last updated:
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2012-05-10 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/108051 |
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Reference:
|
[1] Atici F. M., Gusenov G. Sh.: Positive periodic solutions for nonlinear difference equations with periodic coefficients.J. Math. Anal. Appl. 232 (1999), 166–182. MR 1683041 |
Reference:
|
[2] Atici F. M., Cabada A.: Existence and uniqueness results for discrete second order periodic boundary value problems.Comput. Math. Appl. 45 (2003), 1417–1427. Zbl 1057.39008, MR 2000606 |
Reference:
|
[3] Deimling K.: Nonlinear Functional Analysis.Springer-Verlag, New York, 1985. Zbl 0559.47040, MR 0787404 |
Reference:
|
[4] Guo Z., Yu J.: The existence of periodic and subharmonic solutions for second order superlinear difference equations.Science in China (Series A) 3 (2003), 226–235. MR 2014482 |
Reference:
|
[5] Jiang D., O’Regan D., Agarwal R. P.: Optimal existence theory for single and multiple positive periodic solutions to functional difference equations.Appl. Math. Lett. 161 (2005), 441–462. Zbl 1068.39009, MR 2112417 |
Reference:
|
[6] Kocic V. L., Ladas G.: Global behivior of nonlinear difference equations of higher order with applications.Kluwer Academic Publishers, Dordrecht-Boston-London, 1993. MR 1247956 |
Reference:
|
[7] Ma M., Yu J.: Existence of multiple positive periodic solutions for nonlinear functional difference equations.J. Math. Anal. Appl. 305 (2005), 483–490. Zbl 1070.39019, MR 2130716 |
Reference:
|
[8] Mickens R. E.: Periodic solutions of second order nonlinear difference equations containing a small parameter-II. Equivalent linearization.J. Franklin Inst. B 320 (1985), 169–174. Zbl 0589.39004, MR 0818865 |
Reference:
|
[9] Mickens R. E.: Periodic solutions of second order nonlinear difference equations containing a small parameter-III. Perturbation theory.J. Franklin Inst. B 321 (1986), 39–47. Zbl 0592.39005, MR 0825907 |
Reference:
|
[10] Mickens R. E.: Periodic solutions of second order nonlinear difference equations containing a small parameter-IV. Multi-discrete time method.J. Franklin Inst. B 324 (1987), 263–271. Zbl 0629.39002, MR 0910641 |
Reference:
|
[11] Raffoul Y. N.: Positive periodic solutions for scalar and vector nonlinear difference equations.Pan-American J. Math. 9 (1999), 97–111. |
Reference:
|
[12] Wang Y., Shi Y.: Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions.J. Math. Anal. Appl. 309 (2005), 56–69. Zbl 1083.39019, MR 2154027 |
Reference:
|
[13] Zeng Z.: Existence of positive periodic solutions for a class of nonautonomous difference equations.Electronic J. Differential Equations 3 (2006), 1–18. Zbl 1093.39014, MR 2198916 |
Reference:
|
[14] Zhang R., Wang Z., Chen Y., Wu J.: Periodic solutions of a single species discrete population model with periodic harvest/stock.Comput. Math. Appl. 39 (2000), 77–90. Zbl 0970.92019, MR 1729420 |
Reference:
|
[15] Zhu L., Li Y.: Positive periodic solutions of higher-dimensional functional difference equations with a parameter.J. Math. Anal. Appl. 290 (2004), 654–664. Zbl 1042.39005, MR 2033049 |
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