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Bibliography

B-C-N
H. Brezis, J.M. Coron and L. Nirenberg, Free vibrations of a nonlinear wave equation and a theorem of P. Rabinowitz, Comm. Pure Appl. Math. Vol. 33 (1980), 667-684.

BN-Ma
K. Ben-Naoum and J. Mawhin, The periodic Dirichlet problem for some semilinear wave equations, J. Differential Equations, Vol. 96 (1992), 340-354.

H
M. R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle ^ a des rotations, Publ. I.H.E.S., n 49 (1979), 5-233.

Kh
A. Ya. Khinchin, Continued Fractions, The University of Chicago Press (1964).

Mc
P. J. Mckenna, On solutions of a nonlinear wave equation when the ratio of the period to the length of the interval is irrational, Proc. of AMS, Vol. 93, No.1 (1985), 59-64.

R1
P. H. Rabinowitz, Periodic solutions of nonlinear hyperbolic partial diffrential equations, Comm. Pure Appl. Math. Vol. 20 (1967), 145-205.

R2
P. H. Rabinowitz, Free vibrations for a semilinear wave equations, Comm. Pure Appl. Math. Vol. 31 (1978), 31-68.

W
C.E. Wayne, Periodic and quasiperiodic solutions of nonlinear wave equations via KAM theory, Comm. Math. Phys. Vol. 127 (1990), 479-528.

Ya1
M. Yamaguchi, Quasiperiodic motions of vibrating string with periodically moving boundaries, J. Differential Equations, Vol. 135, No.1 (1997), 1-15.

Ya2
M. Yamaguchi, Periodic motions of vibrating string with a periodically moving boundary, Discrete and Continuous Dynamical Systems, Proceedings of International Conference on Dynamical Systems and Differetial Equations, Vol.2, South Missouri State University, (1998), 303-314.

Ya3
M. Yamaguchi, Quasiperiodic behavior of vibrating string with the Lissajous boundary condition, Functional Analysis and Global Analysis, Proceedings of International Conference on Functional Analysis and Global Analysis (Springer), (1997), 278-287.

Ya4
M. Yamaguchi, Vibrating string problem with quasiperiodically moving boundaries, preprint.

Ya5
M. Yamaguchi, Existence of periodic solutions of second order nonlinear evolution equations and applications, Funkcialaj Ekvacioj, Vol. 38, No.3 (1995), 519-538.

Ya6
M. Yamaguchi, 3D wave equations in sphere-symmetric domain with periodically oscillating boundaries, Discrete and Continuous Dynamical Systems, Vol. 7, no. 2 (2001), 385-396.

Ya7
M. Yamaguchi, Existence and stability of global bounded classical solutions of initial boundary value problem for semilinear wave equations, Funkcialaj Ekvacioj, Vol. 23 (1980), 289-308.

Ya8
M. Yamaguchi, Nonexistence of bounded solutions of one dimensional wave equations with quasiperiodic forcing terms, J. Differential Equations, Vol. 127, No.2 (1996), 484-497.

Ya-Yo
M. Yamaguchi and H. Yoshida, Nonhomogeneous string problem with periodically moving boundaries, Fields Institute Communications, Vol. 25 (2000), 565-574.

Yoc
J.-C. Yoccoz, Conjugaison différentiable des difféomorphismes du cercle dont le nomble de rotation vérifie une condition Diophantienne, Ann. Sci. Ecole Normale Sup., Vol. 17 (1984), 333-359.

Masaru Yamaguchi, Department of Mathematics, Faculty of Science, Tokai University, Kanagawa 259-1292, Japan. E-mail: yamaguchi@sm.u-tokai.ac.jp



Nobuki Takayama 2003-01-30