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Asymptotic solutions of systems of nonlinear difference equations

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Bibliography

  1. Culmer, W. J. A., & W. A. Harris, jr., Convergent solutions of ordinary linear homogeneous difference equations. Pac. J. Math., (to appear).

  2. Harris, W. A., jr., Equivalent classes of difference equations. Contributions to Differential Equations 2, 253–264 (1963).

    Google Scholar 

  3. Horn, J., Zur Theorie der nichtlinearen Differenzengleichungen. J. für reine u. angew. Math. 141, 182–216 (1912).

    Google Scholar 

  4. Horn, J., Laplace-Integrale als Lösungen von Funktionalgleichungen. J. für reine u. angew. Math. 146, 95–115 (1916).

    Google Scholar 

  5. Horn, J., Über eine nichtlineare Differenzengleichung. Jahresb. deutsch. Math. Ver. 26, 230–251 (1918).

    Google Scholar 

  6. Hukuhara, M., Sur l'éxistence des points invariants d'une transformation dans l'espace fonctionnel. Japanese J. Math. 20, 1–4 (1950).

    Google Scholar 

  7. Iwano, M., Intégration analytique d'un système d'équations différentielles non linéaires dans le voisinage d'un point singulier. I; II. Annali Mat. Pura Appl. (44), 261–292 (1957); (47), 91–150 (1959).

  8. Sibuya, Y., On nonlinear differential equations containing a parameter. J. Math. Mech. 9, 369–398 (1960).

    Google Scholar 

  9. Tanaka, S., On asymptotic solutions of non-linear difference equations. I; II; III. Mem. Fac. Sci. Kyusyu Univ. (A) 7, 101–127 (1953); 10, 45–83 (1956); 11, 167–184 (1957).

    Google Scholar 

  10. Trjitzinsky, W. J., Nonlinear difference equations. Compositio Math. 5, 1–60 (1937/38).

    Google Scholar 

  11. Tychonoff, A., Über einen Fixpunktsatz. Math. Ann. III, 767–776 (1935).

    Google Scholar 

  12. Wasow, W., Solution of nonlinear differential equations with a parameter by asymptotic series. Ann. of Math. 69, 485–509 (1959).

    Google Scholar 

  13. Williams, K. P., The solution of nonhomogeneous linear difference equations and their asymptotic form. Trans. A. M. S. 14, 209–240 (1913).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Technology University of Minnesota, Minnesota

    W. A. Harris Jr. & Y. Sibuya

  2. Ochanomizu University, Tokyo

    W. A. Harris Jr. & Y. Sibuya

Authors
  1. W. A. Harris Jr.
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  2. Y. Sibuya
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Additional information

Communicated by A. Erdélyi

The work of W. A. Harris, jr., presented here was supported in part by the U.S.National Science Foundation under Grant G-18918; that of Y. Sibuya, by the U.S.Office of Naval Research, Nonr-3776(00).

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Harris, W.A., Sibuya, Y. Asymptotic solutions of systems of nonlinear difference equations. Arch. Rational Mech. Anal. 15, 377–395 (1964). https://doi.org/10.1007/BF00256928

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  • DOI: https://doi.org/10.1007/BF00256928

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