MR2547106 Masaru YAMAGUCHI Masaru YAMAGUCHI Existence and Regularity of Periodic Solutions of Nonlinear Equations of a Suspended String Funkcialaj Ekvacioj. Serio Internacia 52 2009 281--300 http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-2/52_281.pdf http://www.ams.org/mathscinet-getitem?mr=MR2547106 We shall consider BVP to a nonlinear equation of suspended string with a special power density of order $1/2$ to which a nonlinear time-independent outer force operates. We shall show the existence and the regularity of a family of infinitely many smooth time-periodic solutions of BVP near each normal mode. By considering our BVP in the Sobolev-type function spaces with weights at the origin, we show that under the weak Poincare-type Diophantine condition, the regularity of the solutions coincides with the differentiability of the nonlinear forcing term. The set of the periods is contained in a neighborhood of each period of normal mode, and is uncountable and dense in the interval, and has the Lebesgue measure zero. Periodic solutions, Equation of a suspended string, Diophantine inequality. 35B10, 35L20. 52-281 2009 Existence and Regularity of Periodic Solutions of Nonlinear Equations of a Suspended String Masaru YAMAGUCHI Masaru YAMAGUCHI
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