Periodic solutions of second order nonlinear functional difference equations
Liu, Yuji
Archivum Mathematicum, Tome 043 (2007), p. 67-74 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 2007-01-01
Classification:  39A11,  47N20 
@article{108051,
     author = {Yuji Liu},
     title = {Periodic solutions of second order nonlinear functional difference equations},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {67-74},
     zbl = {1164.39005},
     mrnumber = {2310126},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108051}
}

Liu, Yuji. Periodic solutions of second order nonlinear functional difference equations. Archivum Mathematicum, Tome 043 (2007) pp. 67-74. http://gdmltest.u-ga.fr/item/108051/

Atici F. M.; Gusenov G. Sh. Positive periodic solutions for nonlinear difference equations with periodic coefficients, J. Math. Anal. Appl. 232 (1999), 166–182. (1999) | MR 1683041

Atici F. M.; Cabada A. Existence and uniqueness results for discrete second order periodic boundary value problems, Comput. Math. Appl. 45 (2003), 1417–1427. | MR 2000606 | Zbl 1057.39008

Deimling K. Nonlinear Functional Analysis, Springer-Verlag, New York, 1985. (1985) | MR 0787404 | Zbl 0559.47040

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

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. | MR 2112417 | Zbl 1068.39009

Kocic V. L.; Ladas G. Global behivior of nonlinear difference equations of higher order with applications, Kluwer Academic Publishers, Dordrecht-Boston-London, 1993. (1993) | MR 1247956

Ma M.; Yu J. Existence of multiple positive periodic solutions for nonlinear functional difference equations, J. Math. Anal. Appl. 305 (2005), 483–490. | MR 2130716 | Zbl 1070.39019

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. (1985) | MR 0818865 | Zbl 0589.39004

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. (1986) | MR 0825907 | Zbl 0592.39005

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. (1987) | MR 0910641 | Zbl 0629.39002

Raffoul Y. N. Positive periodic solutions for scalar and vector nonlinear difference equations, Pan-American J. Math. 9 (1999), 97–111. (1999)

Wang Y.; Shi Y. Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions, J. Math. Anal. Appl. 309 (2005), 56–69. | MR 2154027 | Zbl 1083.39019

Zeng Z. Existence of positive periodic solutions for a class of nonautonomous difference equations, Electronic J. Differential Equations 3 (2006), 1–18. | MR 2198916 | Zbl 1093.39014

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. | MR 1729420 | Zbl 0970.92019

Zhu L.; Li Y. Positive periodic solutions of higher-dimensional functional difference equations with a parameter, J. Math. Anal. Appl. 290 (2004), 654–664. | MR 2033049 | Zbl 1042.39005