Abstract
In this paper, the existence of anti-periodic solutions for high order Duffing equations is studied by using degree theory and some known results are improved to some extent.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aftabizadeh, A.R., Aizicovici, S., Pavel, N.H.: On a class of second-order anti-periodic boundary value problems. J. Math. Anal. Appl. 171, 301–320 (1992)
Cong, F.Z., Hunang, Q.D., Shi, S.Y.: Existence and uniqueness of periodic solutions for (2n+1)th order differential equations. J. Math. Anal. Appl. 241, 1–9 (2000)
Deimling, K.: Nonlinear Functional Analysis. Springer, New York (1985)
Hardy, G.H., Littlewood, J.E., Pòlya, G.: Inequalities. Cambridge University Press, Cambridge (1952)
Liu, W.B., Li, Y.: The existence of periodic solutions for high order Duffing equations. Acta. Math. Sin. 46, 49–56 (2003)
Li, W.G.: Periodic solutions for 2kth order ordinary differential equation with resonance. J. Math. Anal. Appl. 259, 157–167 (2001)
Mawhin, J.: Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations. J. Differ. Equ. 52, 264–287 (1984)
Nakao, M.: Existence of an anti-periodic solution for the quasi-linear wave with viscosity. J. Math. Anal. 204, 754–764 (1996)
Ortega, R.: Counting periodic solutions of the forced pendulum equation. Nonlinear Anal. 42, 1055–1062 (2000)
Pinsky, M.A., Zevin, A.A.: Oscillations of a pendulum with a periodically varying length and a model of swing. J. Non-Linear Mech. 34, 105–109 (1999)
Tian, Y., Zhang, G.S., Ge, W.G.: Periodic solutions for a quasilinear non-autonomous second-order system. J. Appl. Math. Comput. 22, 263–271 (2006)
Wang, Y.Y., Zhang, G.S., Ge, W.G.: Multi-point boundary value problems for one-dimensional p-Laplacian at resonance. J. Appl. Math. Comput. 22, 361–372 (2006)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by Science Foundation of China University of Mining and Technology (No. A200403, No. 2005A041 and No. 2006A042).
Rights and permissions
About this article
Cite this article
Chen, T., Liu, W. & Zhang, J. The existence of anti-periodic solutions for high order Duffing equation. J. Appl. Math. Comput. 27, 271–280 (2008). https://doi.org/10.1007/s12190-008-0056-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12190-008-0056-1