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Existence of Periodic Solutions of an Autonomous Damped Wave Equation in Thin Domains

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Abstract

For a nonlinear autonomous damped wave equation in a thin domain we provide conditions ensuring the existence of periodic solutions in time. Our approach uses both methods developed by Hale and Raugel and methods based on the topological degree theory together with some results on the functionalization of parameter.

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Authors and Affiliations

  1. Università degli Studi di Firenze, Facoltà di Ingegneria, Dipartimento di Sistemi e Informatica, Via di S. Marta 3, 50139, Firenze (, Italy)

    Russell Johnson & Paolo Nistri

  2. Department of Mathematics, Universitetskaja p.1, Voronezh State University, Voronezh (, Russia)

    Mikhail Kamenskii

Authors
  1. Russell Johnson
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  2. Mikhail Kamenskii
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  3. Paolo Nistri
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Johnson, R., Kamenskii, M. & Nistri, P. Existence of Periodic Solutions of an Autonomous Damped Wave Equation in Thin Domains. Journal of Dynamics and Differential Equations 10, 409–424 (1998). https://doi.org/10.1023/A:1022601213052

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