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<p>In the present paper, the asymptotic analysis of the first two eigenvalues and eigenfunctions on the jump set is established by exploring the asymptotic trends of stationary points and zero points of relevant eigenfunctions. The results indicate that the first two eigenvalues and eigenfunctions are quite sensitive to the values of the potential near the endpoints. As an application, for reaction diffusion equations arising from river population models, quantitative asymptotic estimations of the first and second eigenvalues with respect to the parameters in boundary conditions are studied. A new proof of the eigenvalue dependence regarding to parameters on the jump set is proposed.</p>

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Asymptotic Analysis of the First Two Eigenvalues for Sturm-Liouville Problems with Two Parameters on the Jump Set with Applications

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Jiangang Qi,
  • Chunyan Sun,
  • Xinyu Zhang

摘要

In the present paper, the asymptotic analysis of the first two eigenvalues and eigenfunctions on the jump set is established by exploring the asymptotic trends of stationary points and zero points of relevant eigenfunctions. The results indicate that the first two eigenvalues and eigenfunctions are quite sensitive to the values of the potential near the endpoints. As an application, for reaction diffusion equations arising from river population models, quantitative asymptotic estimations of the first and second eigenvalues with respect to the parameters in boundary conditions are studied. A new proof of the eigenvalue dependence regarding to parameters on the jump set is proposed.