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Existence of periodic and subharmonic solutions for second-order superlinear difference equations. (English) Zbl 1215.39001
Summary: By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations Δ 2 x n-1 +f(n,x n )=0, some new results are obtained for the above problems when f(t,z) has superlinear growth at zero and at infinity in z.
MSC:
39A05General theory of difference equations
References:
[1]Agarwal, R. P., Difference Equations and Inequalities: Theory, Methods and Applications, New York: Marcel Dekker, 1992.
[2]Erbe, L. H., Xia, H., Yu, J. S., Global stability of a linear nonautonomous delay difference equations, J. Diff. Equations Appl., 1995, 1: 151–161. · Zbl 0855.39007 · doi:10.1080/10236199508808016
[3]Györi, I., Ladas, G., Oscillation Theory of Delay Differential Equations with Applications, Oxford: Oxford University Press, 1991.
[4]Kocic, V. L., Ladas, G., Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Boston: Kluwer Academic Publishers, 1993.
[5]Matsunaga, H., Hara, T., Sakata, S., Global attractivity for a nonlinear difference equation with variable delay, Computers Math. Applic., 2001, 41: 543–551. · Zbl 0985.39009 · doi:10.1016/S0898-1221(00)00297-2
[6]Tang, X. H., Yu, J. S., Oscillation of nonlinear delay difference equations, J. Math. Anal. Appl., 2000, 249: 476–490. · Zbl 0963.39021 · doi:10.1006/jmaa.2000.6902
[7]Yu, J. S., Asymptotic stability for a linear difference equation with variable delay, Computers Math. Applic., 1998, 36: 203–210. · Zbl 0933.39009 · doi:10.1016/S0898-1221(98)80021-7
[8]Zhou, Z., Zhang, Q., Uniform stability of nonlinear difference systems, J. Math. Anal. Appl., 1998, 225: 486–500. · Zbl 0910.39003 · doi:10.1006/jmaa.1998.6039
[9]Elaydi, S. N., Zhang, S., Stability and periodicity of difference equations with finite delay, Funkcialaj Ekvac., 1994, 37: 401–413.
[10]Chang, K. C., Critical Point Theory and Its Applications (in Chinese), Shanghai: Shanghai Science and Technical Press, 1986.
[11]Chang, K. C., Infinite Dimensional Morse Theory and Multiple Solution Problems, Boston: Birkhäuser, 1993.
[12]Kaplanm, J. L., Yorke, J. A., Ordinary differential equations which yield periodic solution of delay differential equations, J. Math. Anal. Appl., 1974, 48: 317–324. · Zbl 0293.34102 · doi:10.1016/0022-247X(74)90162-0
[13]Liu, J. Q., Wang, Z. Q., Remarks on subharmonics with minimal periods of Hamiltonian systems, Nonlinear. Anal. T. M. A., 1993, 7: 803–821. · Zbl 0789.58030 · doi:10.1016/0362-546X(93)90070-9
[14]Mawhin, J., Willem, M., Critical Point Theory and Hamiltonian Systems, New York: Spinger-Verlag Inc., 1989.
[15]Michalek, R., Tarantello, G., Subharmonic solutions with prescribed minimal period for nonautonomous Hamiltonian systems, J. Differential Equations, 1988, 72: 28–55. · Zbl 0645.34038 · doi:10.1016/0022-0396(88)90148-9
[16]Rabinowitz, P. H., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS. AMS 65, 1986.
[17]Capietto, A., Mawhin, J., Zanolin, F., A continuation approach to superlinear periodic boundary value problems, J. Differential Equations, 1990, 88: 347–395. · Zbl 0718.34053 · doi:10.1016/0022-0396(90)90102-U
[18]Hale, J. K., Mawhin, J., Coincidence degree and periodic solutions of neutral equations, J. Differential Equations, 1974, 15: 295–307. · Zbl 0274.34070 · doi:10.1016/0022-0396(74)90081-3
[19]Elaydi, S. N., An Introduction to Difference Equations, New York: Springer-Verlag, 1999.
[20]Pielou, E. C., An Introduction to Mathematical Ecology, New York: Willey Interscience, 1969.
[21]Palais, R. S., Smale, S., A generalized Morse theory, Bull. Amer. Math. Soc., 1964, 70: 165–171. · Zbl 0119.09201 · doi:10.1090/S0002-9904-1964-11062-4