The periodic solutions of a nonhomogeneous string with Dirichlet-Neumann condition
Chinese Annals of Mathematics, Series B(2014)
Abstract
This paper deals with the existence of periodic solutions of a nonhomogeneous string with Dirichlet-Neumann condition. The authors consider the case that the period is irrational multiple of space length and prove that for some irrational number, zero is not the accumulation point of the spectrum of the associated linear operator. This result can be used to prove the existence of the periodic solution avoid using Nash-Moser iteration.
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Key words
Nonhomogeneous string,Periodic solutions,Weak solution,Continued fraction,Lagrange constant
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