Explicit sharp bounds for all nodes of Sturm-Liouville operators with potentials in L¹ balls

2025/12/20 by Jifeng Chu, Chu, Jifeng, Shuyuan Guo +5
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering

paper · doi:10.48550/arxiv.2512.18404

Abstract

For the classical Sturm-Liouville operators, we prove the sharp bounds for all nodes of eigenfunctions by regarding these nodes as nonlinear functionals of potential q∈ L¹[0,1]. By studying the optimization problems to minimize or to maximize the nodes \ T_i,m\ subject to the constraint ‖q‖₁=r with r>0 and using the strong continuity of the nodes in potentials, we obtain the explicit expressions for the sharp bounds, which are given as elementary functions.

Citations

• A novel and application-oriented inverse nodal problem for Sturm-Liouville operators
• On the Second-order Frechet Derivatives of Eigenvalues of Sturm-Liouville Problems in Potentials
• Quantitative Projections in the Sturm Oscillation Theorem

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