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On solutions of a nonlinear wave question when the ratio of the period to the length of the interval is irrational


Author: P. J. McKenna
Journal: Proc. Amer. Math. Soc. 93 (1985), 59-64
MSC: Primary 35B10; Secondary 35L70
DOI: https://doi.org/10.1090/S0002-9939-1985-0766527-X
MathSciNet review: 766527
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Abstract | References | Similar Articles | Additional Information

Abstract: The semilinear wave equation $ {u_{tt}} - {u_{xx}} + f(u) = g(t)$ with $ u(0,t) = u(\pi ,t) = 0$, $ u$ is $ T$-periodic in $ t$, is considered for some situations in which $ T$ is not a rational multiple of $ \pi $. Various existence results depending on the range of $ f'$ are given, which contrast sharply with the case where $ T$ is a rational multiple of $ \pi $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0766527-X
Keywords: Boundary value problems, hyperbolic contractions, compactness
Article copyright: © Copyright 1985 American Mathematical Society

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