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<top_article>
<mrnumber>MR1975054</mrnumber>
<author>Masaru YAMAGUCHI</author>
<author_utf8>Masaru YAMAGUCHI</author_utf8>
<title>Periodic Solutions of Nonlinear Equations of String with Periodically Oscillating Boundaries</title>
<journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
<volume>45</volume>
<year>2002</year>
<page>397--416</page>
<url_pdf>http://fe.math.kobe-u.ac.jp/FE/FullPapers/vol45/fe45-3-5.pdf</url_pdf>
<mathsci_link>http://www.ams.org/mathscinet-getitem?mr=MR1975054</mathsci_link>
<fesi_info>
  <FILE>45-397</FILE>
  <YEAR>2002</YEAR>
  <TITLE>Periodic Solutions of Nonlinear Equations of String with Periodically Oscillating Boundaries</TITLE>
  <AUTHOR>Masaru YAMAGUCHI</AUTHOR>
  <AUTHOR_utf8>Masaru YAMAGUCHI</AUTHOR_utf8>
</fesi_info>

<references>

<article>
<bibitem>1</bibitem>
<author>Brezis, H.; Coron, J. M.; Nirenberg, L.</author>
<title>Free vibrations of a nonlinear wave equation and a theorem of P. Rabinowitz</title>
<journal>Comm. Pure Appl. Math.</journal>
<vol>33</vol>
<year>1980</year>
<page>667-684</page>
<mr>MR0586417</mr>
</article>

<article>
<bibitem>2</bibitem>
<author>Ben-Naoum, K.; Mawhin, J.</author>
<title>The periodic Dirichlet problem for some semilinear wave equations</title>
<journal>J. Differential Equations</journal>
<vol>96</vol>
<year>1992</year>
<page>340-354</page>
<mr>MR1156665</mr>
</article>

<article>
<bibitem>3</bibitem>
<author>Herman, M. R.</author>
<title>Sur la conjugaison differentiable des diffeomorphismes du cercle A des rotations</title>
<journal>Publ. I.H.E.S.</journal>
<vol>49</vol>
<year>1979</year>
<page>5-233</page>
<mr>MR0538680</mr>
</article>

<book>
<bibitem>4</bibitem>
<author>Khinchin, A. Ya.</author>
<booktitle>Continued Fractions</booktitle>
<publisher>The University of Chicago Press</publisher>
<year>1964</year>
<mr>MR0161833</mr>
</book>

<article>
<bibitem>5</bibitem>
<author>Mckenna, P. J.</author>
<title>On solutions of a nonlinear wave equation when the ratio of the period to the length of the interval is irrational</title>
<journal>Proc. of AMS</journal>
<vol>93</vol>
<year>1985</year>
<page>59-64</page>
<mr>MR0766527</mr>
</article>

<article>
<bibitem>6</bibitem>
<author>Rabinowitz, P. H.</author>
<title>Periodic solutions of nonlinear hyperbolic partial diffrential equations</title>
<journal>Comm. Pure Appl. Math.</journal>
<vol>20</vol>
<year>1967</year>
<page>145-205</page>
<mr>MR0206507</mr>
</article>

<article>
<bibitem>7</bibitem>
<author>Rabinowitz, P. H.</author>
<title>Free vibrations for a semilinear wave equations</title>
<journal>Comm. Pure Appl. Math.</journal>
<vol>31</vol>
<year>1978</year>
<page>31-68</page>
<mr>MR0470378</mr>
</article>

<article>
<bibitem>8</bibitem>
<author>Wayne, C. E.</author>
<title>Periodic and quasiperiodic solutions of nonlinear wave equations via KAM theory</title>
<journal>Comm. Math. Phys.</journal>
<vol>127</vol>
<year>1990</year>
<page>479-528</page>
<mr>MR1040892</mr>
</article>

<article>
<bibitem>9</bibitem>
<author>Yamaguchi, M.</author>
<title>Quasiperiodic motions of vibrating string with periodically moving boundaries</title>
<journal>J. Differential Equations</journal>
<vol>135</vol>
<year>1997</year>
<page>1-15</page>
<mr>MR1434912</mr>
</article>

<article>
<bibitem>10</bibitem>
<author>Yamaguchi, M.</author>
<title>Periodic motions of vibrating string with a periodically moving boundary</title>
<journal>Discrete and Continuous Dynamical systems, Proceedings of International Conference on Dynamical Systems and Differetial Equations, South Missouri State University</journal>
<vol>2</vol>
<year>1998</year>
<page>303-314</page>
<mr>MR1722479</mr>
</article>

<article>
<bibitem>11</bibitem>
<author>Yamaguchi, M.</author>
<title>Quasiperiodic behavior of vibrating string with the Lissajous boundary condition</title>
<journal>Functional Analysis and Global Analysis, Proceedings of International Conference on Functional Analysis and Global Analysis Springer</journal>
<year>1997</year>
<page>278-287</page>
<mr>MR1658069</mr>
</article>

<other>
<bibitem>12</bibitem>
<raw_data>Yamaguchi, M., Vibrating string problem with quasiperiodically moving boundaries, preprint</raw_data>
</other>

<fearticle>
<bibitem>13</bibitem>
<author>Yamaguchi, M.</author>
<title>Existence of periodic solutions of second order nonlinear evolution equations and applications</title>
<journal>Funkcialaj Ekvacioj</journal>
<vol>38</vol>
<year>1995</year>
<page>519-538</page>
<mr>MR1374435</mr>
<feart>1374435</feart>
</fearticle>

<article>
<bibitem>14</bibitem>
<author>Yamaguchi, M.</author>
<title>3D wave equations in sphere-symmetric domain with periodically oscillating boundaries</title>
<journal>Discrete and Continuous Dynamical Systems</journal>
<vol>7</vol>
<year>2001</year>
<page>385-396</page>
<mr>MR1808409</mr>
</article>

<fearticle>
<bibitem>15</bibitem>
<author>Yamaguchi, M.</author>
<title>Existence and stability of global bounded classical solutions of initial boundary value problem for semilinear wave equations</title>
<journal>Funkcialaj Ekvacioj</journal>
<vol>23</vol>
<year>1980</year>
<page>289-308</page>
<mr>MR0621535</mr>
<feart>0621535</feart>
</fearticle>

<article>
<bibitem>16</bibitem>
<author>Yamaguchi, M.</author>
<title>Nonexistence of bounded solutions of one dimensional wave equations with quasiperiodic forcing terms</title>
<journal>J. Differential Equations</journal>
<vol>127</vol>
<year>1996</year>
<page>484-497</page>
<mr>MR1389406</mr>
</article>

<article>
<bibitem>17</bibitem>
<author>Yamaguchi, M.; Yoshida, H.</author>
<title>Nonhomogeneous string problem with periodically moving boundaries</title>
<journal>Fields Institute Communications</journal>
<vol>25</vol>
<year>2000</year>
<page>565-574</page>
<mr>MR1759569</mr>
</article>

<article>
<bibitem>18</bibitem>
<author>Yoccoz, J.-C.</author>
<title>Conjugaison differentiable des diffeomorphismes du cercle dont le nomble de rotation verifie une condition Diophantienne</title>
<journal>Ann. Sci. Ecole Normale Sup.</journal>
<vol>17</vol>
<year>1984</year>
<page>333-359</page>
<mr>MR0777374</mr>
</article>

</references>
</top_article>
