Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

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)
  • Published : 2010.05.01
Download PDF
⟨ Previous Next ⟩

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

References

  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. https://doi.org/10.1016/0022-247X(92)90345-E
  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. https://doi.org/10.1006/jmaa.1999.6471
  4. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
  5. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, 1952.
  6. 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.
  7. W. G. Li, Periodic solutions for 2kth order ordinary differential equations with resonance, J. Math. Anal. Appl. 259 (2001), no. 1, 157-167. https://doi.org/10.1006/jmaa.2000.7407
  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. 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. https://doi.org/10.1016/0022-0396(84)90180-3
  10. 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. https://doi.org/10.1006/jmaa.1996.0465
  11. R. Ortega, Counting periodic solutions of the forced pendulum equation, Nonlinear Anal. 42 (2000), no. 6, Ser. A: Theory Methods, 1055-1062. https://doi.org/10.1016/S0362-546X(99)00169-8
  12. 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. https://doi.org/10.1016/S0020-7462(98)00005-5

Cited by

  1. Existence of anti-periodic solutions for second-order ordinary differential equations involving the Fučík spectrum vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-2770-2012-149
  2. ANTI-PERIODIC SOLUTIONS FOR HIGHER-ORDER LIÉENARD TYPE DIFFERENTIAL EQUATION WITH p-LAPLACIAN OPERATOR vol.49, pp.3, 2012, https://doi.org/10.4134/BKMS.2012.49.3.455