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<p>In this paper we study the optimization problems of the first eigenvalue for the fourth-order beam equations with integrable potentials, given the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> norm of the potentials. We reduce these infinite-dimensional optimization problems of implicit functionals to finite-dimensional ones and derive optimal bounds for the first eigenvalue. Our results can be regarded as a contribution to the literature by developing a methodological framework for solving these infinite-dimensional optimization problems.</p>

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Optimal bounds for the first eigenvalue of fourth-order beam equations with integrable potentials

  • 期刊论文

  • 发表日期：

    2025年7月17日

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  • Yongkang Cheng,
  • Gang Meng,
  • Zhi Qian

摘要

In this paper we study the optimization problems of the first eigenvalue for the fourth-order beam equations with integrable potentials, given the \(L^1\) L 1 norm of the potentials. We reduce these infinite-dimensional optimization problems of implicit functionals to finite-dimensional ones and derive optimal bounds for the first eigenvalue. Our results can be regarded as a contribution to the literature by developing a methodological framework for solving these infinite-dimensional optimization problems.