Meromorphic solutions of some nonlinear difference equations of higher order

Niro YANAGIHARA

doi:10.2969/jmsj/03740569

Niro YANAGIHARA

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JOURNAL FREE ACCESS

1985 Volume 37 Issue 4 Pages 569-603

DOI https://doi.org/10.2969/jmsj/03740569

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Published: 1985 Received: May 04, 1984 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W.A. Harris, jr. and Y. Sibuya, Asymptotic solutions of systems of nonlinear difference equations, Arch. Rational Mech. Anal., 15 (1964), 377-395.
2) W.A. Harris, jr. and Y. Sibuya, On asymptotic solutions of systems of nonlinear difference equations, J. Reine Angew. Math., 222 (1966), 120-135.
3) M. Hukuhara, Sur l'existence des points invariants d'une transformation dans l'espace fonctionnel, Japan. J. Math., 20 (1950), 1-4.
4) G. Julia, Memoire sur l'itération des fonctions rationnelles, CEuvres de G. Julia, vol. I, Gauthier-Villars, 1968, 121-319. (J. Math. Pures Appl., 8^e ser., 1 (1918), 47-245.)
5) T. Kimura, On the iterarion of analytic functions, Funkcial. Ekvac., 14 (1971), 197-238.
6) T. Kimura, On meromorphic solutions of the difference equation y(x+1)=y(x)+1+λ/y(x), Lecture Notes in Math., 312 (1973), Springer-Verlag, 74-86.
7) N.E. Nörlund, Vorlesungen über Differenzenrechnung, Chelsea Publ. Co., New York, 1954.
8) O. Perron, Über die Poincarésche lineare Differenzengleichung, J. Reine Angew. Math., 137 (1910), 6-64.
9) O. Perron, Über Summengleichungen und Poincarésche Differenzengleichungen, Math. Ann., 84 (1921), 1-15.
10) N. Yanagihara, Meromorphic solutions of some difference equations, Funkcial. Ekvac., 23 (1980), 309-326.
11) N. Yanagihara, Meromorphic solutions of some difference equations of the n-th order, to appear in Arch. Rational Mech. Anal.

Right : [1] W. A. Harris, jr. and Y. Sibuya, Asymptotic solutions of systems of nonlinear difference equations, Arch. Rational Mech. Anal., 15 (1964), 377-395.
[2] W. A. Harris, jr. and Y. Sibuya, On asymptotic solutions of systems of nonlinear difference equations, J. Reine Angew. Math., 222 (1966), 120-135.
[3] M. Hukuhara, Sur l'existence des points invariants d'une transformation dans l'espace fonctionnel, Japan. J. Math., 20 (1950), 1-4.
[4] G. Julia, Memoire sur l'itération des fonctions rationnelles, CEuvres de G. Julia, vol. I, Gauthier-Villars, 1968, 121-319. (J. Math. Pures Appl., 8^e ser., 1 (1918), 47-245.)
[5] T. Kimura, On the iterarion of analytic functions, Funkcial. Ekvac., 14 (1971), 197-238.
[6] T. Kimura, On meromorphic solutions of the difference equation y(x+1)=y(x)+1+λ/y(x), Lecture Notes in Math., 312 (1973), Springer-Verlag, 74-86.
[7] N. E. Nörlund, Vorlesungen über Differenzenrechnung, Chelsea Publ. Co., New York, 1954.
[8] O. Perron, Über die Poincarésche lineare Differenzengleichung, J. Reine Angew. Math., 137 (1910), 6-64.
[9] O. Perron, Über Summengleichungen und Poincarésche Differenzengleichungen, Math. Ann., 84 (1921), 1-15.
[10] N. Yanagihara, Meromorphic solutions of some difference equations, Funkcial. Ekvac., 23 (1980), 309-326.
[11] N. Yanagihara, Meromorphic solutions of some difference equations of the n-th order, to appear in Arch. Rational Mech. Anal.

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