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Existence of sign-changing periodic solutions of second order difference equations. (English) Zbl 1186.39018
This work is based on a paper by the first author [Global bifurcation of periodic solutions to second order ordinary differential equations, accepted in Acta Math. Sci. B], where the existence of nodal solutions of nonlinear periodic boundary value problems of ODE $$u''+ rf(u)=0,~ u(t+2\pi)=u(t)$$ is investigated. In this paper a discrete analogue is considered and it is answered that the similar results are still true.

39A23Periodic solutions (difference equations)
Full Text: DOI
[1] R. Ma, Global bifurcation of periodic solutions to second order ordinary differential equations, Acta Math. Sci. B (accepted for publication). · Zbl 1212.34025
[2] Ma, R.; Ma, H.: Unbounded perturbations of nonlinear discrete periodic problem at resonance. Nonlinear anal. TMA (2008) · Zbl 1166.39008
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[4] Atici, F. M.; Guseinov, G. Sh.: Positive periodic solutions for nonlinear difference equations with periodic coefficients. J. math. Anal. appl. 232, 166-182 (1999) · Zbl 0923.39010
[5] Atici, F. M.; Cabada, A.: Existence and uniqueness results for discrete second-order periodic boundary value problems. Comput. math. Appl. 45, 1417-1427 (2003) · Zbl 1057.39008
[6] Agarwal, R. P.; O’regan, D.: Boundary value problems for discrete equations. Appl. math. Lett. 10, 83-89 (1997) · Zbl 0890.39001
[7] Thompson, H. B.; Tisdell, C.: Systems of difference equations associated with boundary value problems for second-order systems of ordinary differential equations. J. math. Anal. appl. 248, 333-347 (2000) · Zbl 0963.65081
[8] Rachunkova, I.; Tisdell, C. C.: Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions. Nonlinear anal. TMA 67, 1236-1245 (2007) · Zbl 1130.39017
[9] Ma, Ruyun: Nonlinear discrete Sturm-Liouville problems at resonance. Nonlinear anal. TMA 67, 3050-3057 (2007) · Zbl 1129.39006
[10] Marlin, J. A.: Periodic motions of coupled simple pendulums with periodic disturbances. Int. J. Nonlinear mech. 3, 439-447 (1968) · Zbl 0169.55605
[11] Coron, J. M.: Periodic solutions of a nonlinear wave equation without monotonicity. Math. ann. 262, 273-285 (1983) · Zbl 0489.35061
[12] Ma, R.; Thompson, B.: Nodal solutions for nonlinear eigenvalue problems. Nonlinear anal. 59, 707-718 (2004) · Zbl 1059.34013