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<p>We consider a&#xa0;Sturm–Liouville problem on [0,&#xa0;1] with Dirichlet boundary conditions and weighted integral conditions on the potential, where one of the conditions assumes that the potential may have singularities of different orders at the end-points of the segment [0,&#xa0;1]. In this paper, we study lower estimates for the first eigenvalue of the problem for different values of the integral condition parameters. Foe some values of these parameters we give a&#xa0;method of finding precise lower estimates.</p>

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ON LOWER ESTIMATES FOR THE FIRST EIGENVALUE OF A STURM–LIOUVILLE PROBLEM WITH WEIGHTED INTEGRAL CONDITIONS ON THE POTENTIAL

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • S. Ezhak,
  • M. Telnova

摘要

We consider a Sturm–Liouville problem on [0, 1] with Dirichlet boundary conditions and weighted integral conditions on the potential, where one of the conditions assumes that the potential may have singularities of different orders at the end-points of the segment [0, 1]. In this paper, we study lower estimates for the first eigenvalue of the problem for different values of the integral condition parameters. Foe some values of these parameters we give a method of finding precise lower estimates.