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Bifurcation problems associated with nonlinear wave propagation

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Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1151))

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References

  1. J. C. Alexander, A primer on connectivity, in Proc. Conf. on Fixed Point Theory, 1980, edited by E. Fadell & G. Fournier, Springer Lecture Notes in Math 886, (1981) 455–483.

    Google Scholar 

  2. J. C. Alexander & S. S. Antman, Global behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problems, Arch. Rational Mech. Anal. 76, (1981) 339–354.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. C. Alexander, S. S. Antman, & S.-T. Deng, Nonlinear eigenvalue problems for the whirling of heavy elastic strings II: New methods of global bifurcation theory. Proc. Roy. Soc. Edinburgh, 93A, (1983) 197–227.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. J. Amick & J. T. Toland, On solitary water-waves of finite amplitude, Arch. Rational Mech. Anal. 76, (1981) 9–95.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. S. Antman, Nonlinear eigenvalue problems for the whirling of heavy elastic strings. Proc. Roy. Soc. Edinburgh, 85A, (1980) 59–85.

    Article  MathSciNet  MATH  Google Scholar 

  6. S. S. Antman & Guo Zhong-Heng, Large shearing oscillations of incompressible nonlinearly elastic bodies, J. Elasticity, (1984) to appear.

    Google Scholar 

  7. S. S. Antman & R. Malek-Madani, Travelling waves in nonlinearly viscoelastic media, in preparation.

    Google Scholar 

  8. S. S. Antman & M. Reeken, The whirling and drawing of strings, to appear.

    Google Scholar 

  9. M. G. Crandall & P. H. Rabinowitz, Nonlinear Sturm-Liouville problems and topological degree, J. Math. Mech. 19, (1970) 1083–1102.

    MathSciNet  MATH  Google Scholar 

  10. M. G. Crandall & P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Functional Anal. 8, (1971) 321–340.

    Article  MathSciNet  MATH  Google Scholar 

  11. P. H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Functional Anal. 7, (1971) 487–513.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, 1983.

    Google Scholar 

  13. W. A. Strauss, Existence of solitary waves in higher dimensions, Commun. Math. Phys. 55, (1977) 149–162.

    Article  MathSciNet  MATH  Google Scholar 

  14. C. A. Stuart, Spectral theory of rotating chains, Proc. Roy. Soc. Edinburgh 73A, (1975) 199–214.

    MathSciNet  MATH  Google Scholar 

  15. G. T. Whyburn, Topological Analysis, Rev. Edn., Princeton Univ. Press, 1964.

    Google Scholar 

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Authors

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Brian D. Sleeman Richard J. Jarvis

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© 1985 Springer-Verlag

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Antman, S.S. (1985). Bifurcation problems associated with nonlinear wave propagation. In: Sleeman, B.D., Jarvis, R.J. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 1151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074711

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  • DOI: https://doi.org/10.1007/BFb0074711

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15694-9

  • Online ISBN: 978-3-540-39640-6

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