Infinitely Many Periodic Solutions of Nonlinear Equations of Suspended Strings

MR2440941 Masaru YAMAGUCHI Masaru YAMAGUCHI Infinitely Many Periodic Solutions of Nonlinear Equations of Suspended Strings Funkcialaj Ekvacioj. Serio Internacia 51 2008 245--267 http://fe.math.kobe-u.ac.jp/FE/FullPapers/51-2/51_245.pdf http://www.ams.org/mathscinet-getitem?mr=MR2440941 We shall deal with a nonlinear equation of a suspended string with a special density to which a nonlinear time-independent external force is applied. We shall show the existence of infinitely many time-periodic solutions, near time-periodic solutions which are independent of position. The set of the periods is constructed by using algebraic numbers of degree $2$ and the continued fractions. Periodic solutions, Equation of a suspended string, Diophantine inequality. 35B10, 35L20. 51-245 2008 Infinitely Many Periodic Solutions of Nonlinear Equations of Suspended Strings Masaru YAMAGUCHI Masaru YAMAGUCHI 1 Adams, R. A. Sobolev Spaces Academic Press 1975 MR0450957 2 Khinchin, A. Ya. Continued Fractions The University of Chicago Press 1964 MR0161833 3 Korenev, B. G. Bessel Functions and Their Applications Taylor and Francis Inc. 2002 MR1963816 4 Koshlyakov, N. S.; Gliner, E. V.; Smirnov, M. M. Differential Equations of Mathematical Physics Moscow 1962 (in Russian). English Translation: North-Holland Publ. Co, 1964 MR0177179

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