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Keywords:
periodic solutions; second order functional difference equation; fixed-point theorem; growth condition
periodic solutions; second order functional difference equation; fixed-point theorem; growth condition
Summary:
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.
References:
[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
[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. MR 2000606 | Zbl 1057.39008
[3] Deimling K.: Nonlinear Functional Analysis. Springer-Verlag, New York, 1985. MR 0787404 | Zbl 0559.47040
[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
[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. MR 2112417 | Zbl 1068.39009
[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
[7] 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
[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. MR 0818865 | Zbl 0589.39004
[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. MR 0825907 | Zbl 0592.39005
[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. MR 0910641 | Zbl 0629.39002
[11] Raffoul Y. N.: Positive periodic solutions for scalar and vector nonlinear difference equations. Pan-American J. Math. 9 (1999), 97–111.
[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. MR 2154027 | Zbl 1083.39019
[13] 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
[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. MR 1729420 | Zbl 0970.92019
[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. MR 2033049 | Zbl 1042.39005
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