Periodic solutions with irrational frequency for a class of semilinear wave equations with variable coefficients
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Published:2023-12-31
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Volume:
Page:1-17
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Abstract
This paper is devoted to the study of the existence of periodic solutions for
a class of semilinear wave equations with variable coefficients. The forced vibrations
of a nonhomogeneous string and propagation of seismic waves in nonisotropic media
is governed by this mathematical model. When the frequency is a sufficiently large
irrational number with bounded partial quotients, the existence of weak solutions
is established. Then, under some suitable conditions, we improve the regularity
of weak solutions. Our results can also be applied to the corresponding constant
coefficients wave equation.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University