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<p>In this paper, we study the existence of periodic solutions for a class of damped vibration problems in an open set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \subset \mathbb {R}^{N}\)</EquationSource> </InlineEquation>. We assume that the potential <i>V</i>(<i>t</i>,&#xa0;<i>x</i>) is singular in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\Omega\)</EquationSource> </InlineEquation>, that is <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(V(t,x)\rightarrow +\infty\)</EquationSource> </InlineEquation> as <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(x\rightarrow \partial \Omega\)</EquationSource> </InlineEquation>. To the best of our knowledge, the damped vibration problems with singular potential has not been considered before. By using the Morse theory, we shall obtain infinitely many periodic solutions.</p>

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Infinitely Many Periodic Solutions for a Class of Damped Vibration Problems with Singular Potential

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Hang Yin,
  • Guanggang Liu

摘要

In this paper, we study the existence of periodic solutions for a class of damped vibration problems in an open set \(\Omega \subset \mathbb {R}^{N}\) . We assume that the potential V(t, x) is singular in \(\Omega\) , that is \(V(t,x)\rightarrow +\infty\) as \(x\rightarrow \partial \Omega\) . To the best of our knowledge, the damped vibration problems with singular potential has not been considered before. By using the Morse theory, we shall obtain infinitely many periodic solutions.