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 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.
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