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<p>The present paper is concerned with the asymptotic behavior of the principal eigenvalue of Sturm-Liouville eigenvalue problems with parameter both in equations and coupled boundary conditions. As the parameter becomes sufficiently large, the existence of the principal eigenvalue is resolved primarily, and the asymptotic state is obtained using the relationship among eigenvalues under different boundary conditions. More specifically, the exact growth order of the principal eigenvalue with respect to the parameter is derived. Numerical simulations of the eigenvalues support the validity of the obtained asymptotic estimates.</p>

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Asymptotic behavior analysis for the principal eigenvalues of Sturm-Liouville problems with a parameter under coupled boundary conditions

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Xinyu Zhang,
  • Jiangang Qi,
  • Chunyan Sun

摘要

The present paper is concerned with the asymptotic behavior of the principal eigenvalue of Sturm-Liouville eigenvalue problems with parameter both in equations and coupled boundary conditions. As the parameter becomes sufficiently large, the existence of the principal eigenvalue is resolved primarily, and the asymptotic state is obtained using the relationship among eigenvalues under different boundary conditions. More specifically, the exact growth order of the principal eigenvalue with respect to the parameter is derived. Numerical simulations of the eigenvalues support the validity of the obtained asymptotic estimates.