Global smooth solutions of IBVP to nonlinear equation of suspended string

Yamaguchi, Masaru

doi:10.1016/j.jmaa.2007.12.048

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Cited by 2 publications

(2 citation statements)

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“…From [K-G-S], Chapter 12 and [Ya4], section 2 the eigenvalues and the corresponding eigenfunctions are…”

Section: Function Spacesmentioning

confidence: 99%

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Existence and Regularity of Periodic Solutions of Nonlinear Equations of a Suspended String

Yamaguchi

2009

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Abstract. 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 di¤erentiability 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.

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“…From [K-G-S], Chapter 12 and [Ya4], section 2 the eigenvalues and the corresponding eigenfunctions are…”

Section: Function Spacesmentioning

confidence: 99%

“…For nonlinear damped equations of suspended string Yamaguchi-Nagai-Matsukane [Ya-Na-Ma] studied the existence of periodic solutions for various nonlinear terms. The global existence of solutions of IBVP to nonlinear eqations of a suspended string is studied by [ and [Ya4].…”

Section: Introductionmentioning

confidence: 99%