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Periodic solutions of some forced Liénard differential equations at resonance

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References

  1. S. H. Chang, Periodic solutions of certain second order nonlinear differential equations. J. Math. Anal. Appl.49, 263–266 (1975).

    Google Scholar 

  2. C. P.Gupta, On functional equations of Fredholm and Hammerstein type with applications to existence of periodic solutions of certain ordinary differential equations. J. Integral Equations, to appear.

  3. A. C. Lazer, On Schauder's fixed point theorem and forced second order nonlinear oscillations. J. Math. Anal. Appl.21, 421–425 (1968).

    Google Scholar 

  4. M. Martelli, On forced nonlinear oscillations. J. Math. Anal. Appl.69, 456–504 (1979).

    Google Scholar 

  5. M. Martelli andJ. D. Schuur, Periodic solutions of Liénard type second-order ordinary differential equations. Tohoku Math. J.32, 201–207 (1980).

    Google Scholar 

  6. J. Mawhin, An extension of a theorem of A. C. Lazer on forced nonlinear equations. J. Math. Anal. Appl.40, 20–29 (1972).

    Google Scholar 

  7. J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems. CBMS Conference in Math., Vol.40, Amer. Math. Soc., Providence, R. I., 1970.

    Google Scholar 

  8. J.Mawhin and J. R.Ward, Jr., Nonuniform nonresonance conditions at the first two eigenvalues for periodic solutions of forced Liénard and Duffing equations. To appear.

  9. R. Reissig, Schwingungssätze für die verallgemeinerte Liénardsche Differentialgleichung. Abh. Math. Sem. Univ. Hamburg44, 45–51 (1975).

    Google Scholar 

  10. R. Reissig, Continua of periodic solutions of the Liénard equation, in “Constructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations”. ISNM48, 126–133, Basel (1979).

    Google Scholar 

  11. R. Reissig, Periodic solutions of a second order differential equations including a onesided restoring term. Arch. Math.33, 85–90 (1979).

    Google Scholar 

  12. K. Schmitt, Periodic solutions of a forced nonlinear oscillator involving a one sided restoring force. Arch. Math.31, 70–73 (1978).

    Google Scholar 

  13. J. R. Ward, Jr., Asymptotic conditions for periodic solutions of ordinary differential equations. Proc. Amer. Math. Soc.81, 415–420 (1981).

    Google Scholar 

  14. J. R. Ward, Jr., Periodic solutions for systems of second order ordinary differential equations. J. Math. Anal. Appl.81, 92–98 (1981).

    Google Scholar 

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Mawhin, J., Ward, J.R. Periodic solutions of some forced Liénard differential equations at resonance. Arch. Math 41, 337–351 (1983). https://doi.org/10.1007/BF01371406

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