Next: About this document ...
Up: Periodic Solutions of Nonlinear
Previous: Introduction
-
- 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