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http://dx.doi.org/10.4134/JKMS.2010.47.3.573

ANTI-PERIODIC SOLUTIONS FOR HIGHER-ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS  

Chen, Tai Yong (DEPARTMENT OF MATHEMATICS CHINA UNIVERSITY OF MINING AND TECHNOLOGY)
Liu, Wen Bin (DEPARTMENT OF MATHEMATICS CHINA UNIVERSITY OF MINING AND TECHNOLOGY)
Zhang, Jian Jun (DEPARTMENT OF MATHEMATICS CHINA UNIVERSITY OF MINING AND TECHNOLOGY)
Zhang, Hui Xing (DEPARTMENT OF MATHEMATICS CHINA UNIVERSITY OF MINING AND TECHNOLOGY)
Publication Information
Journal of the Korean Mathematical Society / v.47, no.3, 2010 , pp. 573-583 More about this Journal
Abstract
In this paper, the existence of anti-periodic solutions for higher-order nonlinear ordinary differential equations is studied by using degree theory and some known results are improved to some extent.
Keywords
higher-order differential equation; anti-periodic solution; Leray-Schauder principle;
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1 A. R. Aftabizadeh, S. Aizicovici, and N. H. Pavel, On a class of second-order antiperiodic boundary value problems, J. Math. Anal. Appl. 171 (1992), no. 2, 301-320.   DOI
2 T. Y. Chen, W. B. Liu, J. J. Zhang, and M. Y. Zhang, Existence of anti-periodic solutions for Lienard equations, J. Math. Study 40 (2007), no. 2, 187-195.
3 F. Z. Cong, Q. D. Hunang, and S. Y. Shi, Existence and uniqueness of periodic solutions for (2n+1)th-order differential equations, J. Math. Anal. Appl. 241 (2000), no. 1, 1-9.   DOI   ScienceOn
4 B. W. Li and L. H. Huang, Existence of periodic solutions for nonlinear nth order ordinary differential equations, Acta Math. Sinica (Chin. Ser.) 47 (2004), no. 6, 1133-1140.
5 W. G. Li, Periodic solutions for 2kth order ordinary differential equations with resonance, J. Math. Anal. Appl. 259 (2001), no. 1, 157-167.   DOI   ScienceOn
6 G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, 1952.
7 J. Mawhin and M. Willem, Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations, J. Differential Equations 52 (1984), no. 2, 264-287.   DOI
8 W. B. Liu and Y. Li, Existence of periodic solutions for higher-order Duffing equations, Acta Math. Sinica (Chin. Ser.) 46 (2003), no. 1, 49-56.
9 M. Nakao, Existence of an anti-periodic solution for the quasilinear wave equation with viscosity, J. Math. Anal. Appl. 204 (1996), no. 3, 754-764.   DOI   ScienceOn
10 K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
11 M. A. Pinsky and A. A. Zevin, Oscillations of a pendulum with a periodically varying length and a model of swing, Internat. J. Non-Linear Mech. 34 (1999), no. 1, 105-109.   DOI   ScienceOn
12 R. Ortega, Counting periodic solutions of the forced pendulum equation, Nonlinear Anal. 42 (2000), no. 6, Ser. A: Theory Methods, 1055-1062.   DOI   ScienceOn