<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="f1.xsl"?>
<top_article>
 <mrnumber>MR0173820</mrnumber>
 <author>Urabe, Minoru</author>
 <author_utf8>Minoru URABE</author_utf8>
 <title>Relations between periods and amplitudes of periodic solutions               of {$\ddot x+g(x)=0$}</title>
 <journal>Funkcialaj Ekvacioj. Serio Internacia</journal>
 <volume>6</volume>
 <year>1964</year>
 <page>63--88</page>
 <url_pdf>http://fe.math.kobe-u.ac.jp/FE/Free/vol06/fe06-6.pdf</url_pdf>
 <url_infty_pdf>http://fe.math.kobe-u.ac.jp/FE/FE_pdf_with_bookmark/FE01-10-en_KML/fe06-063-088/fe06-063-088.pdf</url_infty_pdf>
 <mathsci_link> http://www.ams.org/mathscinet-getitem?mr=MR0173820</mathsci_link>
<fesi_info>
  <FILE>fe06-063-088</FILE>
  <YEAR>1964</YEAR>
  <TITLE>Relations between Periods and Amplitudes of Periodic Solutions of $\ddot{x}+g(x)=0$</TITLE>
  <AUTHOR>URABE, Minoru</AUTHOR>
  <AUTHOR_utf8>URABE, Minoru</AUTHOR_utf8>
</fesi_info>

<references>
  <article>
    <bibitem>1</bibitem>
    <author>Koukles, I.; Piskounov, N.</author>
    <title>Sur les vibrations tautochrones dans les syst&#232;mes conservatifs et non conservatifs</title>
    <journal>C. R. Acad. Sci. URSS</journal>
    <vol>17</vol>
    <year>1937</year>
    <page>471-475</page>
    <not_found>Data is not found in MathSci.</not_found>
    <query_string>Cache/Ko/Koukles,tautochrones,C*,1937,1938</query_string>
  </article>

  <article>
    <bibitem>2</bibitem>
    <author>Opial, Z.</author>
    <title>Sur les p&#233;riodes des solutions de l'&#233;quation differentielle $x''+g(x)=0$</title>
    <journal>Ann. Polon. Math.</journal>
    <vol>10</vol>
    <year>1961</year>
    <page>49-72</page>
    <mr>MR0121544</mr>
    <score>88</score>
    <query_string>Cache/Op/Opial,differentielle,Ann*,1961,1962</query_string>
  </article>

  <article>
    <bibitem>3</bibitem>
    <author>Urabe, M.</author>
    <title>Potential forces which yield periodic motions of a fixed period</title>
    <journal>J. Math. Mech.</journal>
    <vol>10</vol>
    <year>1961</year>
    <page>569-578</page>
    <mr>MR0123060</mr>
    <score>100</score>
    <query_string>Cache/Ur/Urabe,Potential,J*,1961,1962</query_string>
  </article>

  <article>
    <bibitem>4</bibitem>
    <author>Urabe, M.</author>
    <title>The potential force yielding a periodic motion whose period is an arbitrary continuous function of the amplitude of the velocity</title>
    <journal>Arch. Rational Mech. Anal.</journal>
    <vol>11</vol>
    <year>1962</year>
    <page>27-33</page>
    <mr>MR0141834</mr>
    <score>100</score>
    <query_string>Cache/Ur/Urabe,continuous,Arch*,1962,1963</query_string>
  </article>

  <article>
    <bibitem>5</bibitem>
    <author>Urabe, M.</author>
    <title>The potential force yielding a periodic motion whose period is an arbitrary continuously differentiable function of the amplitude</title>
    <journal>J. Sci. Hiroshima Univ., Ser. A-I</journal>
    <ser>A-I</ser>
    <vol>26</vol>
    <year>1962</year>
    <page>93-109</page>
    <mr>MR0150400</mr>
    <score>100</score>
    <query_string>Cache/Ur/Urabe,differentiable,J*,1962,1963</query_string>
  </article>

  <article>
    <bibitem>6</bibitem>
    <author>Urabe, M.</author>
    <title>The potential force yielding a periodic motion with arbitrary continuous half-periods</title>
    <journal>J. Sci. Hiroshima Univ., Ser. A-I</journal>
    <ser>A-I</ser>
    <vol>26</vol>
    <year>1962</year>
    <page>111-122</page>
    <mr>MR0150401</mr>
    <score>100</score>
    <query_string>Cache/Ur/Urabe,half-periods,J*,1962,1963</query_string>
  </article>

  <book>
    <bibitem>7</bibitem>
    <author>Whittaker, E. T.; Watson, G. N.</author>
    <booktitle>A course of modern analysis, 4th ed.</booktitle>
    <year>1927</year>
    <page>229</page>
    <mr>MR0178117</mr>
    <query_string>Cache/Wh/Whittaker,analysis,ed*,1927,1928</query_string>
  </book>

</references>
</top_article>
