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- W3214356764 abstract "In this paper, we prove the optimal lower bound $frac{lambda_n}{lambda_m}geq(frac{n}{m})^2$ of vibrating string $$-y''=lambdarho(x) y,$$ with Dirichlet boundary conditions for concave densities. Our aproach is based on the method of Huang [Proc. AMS., 1999]. The main argument is to restrict the two consecutive eigenfunction $y_{n-1}$ and $y_n$ between two successive zeros of $y_{n-1}$. We also prove the same result for the Dirichlet Sturm-Liouville problems." @default.
- W3214356764 created "2021-11-22" @default.
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- W3214356764 date "2021-11-15" @default.
- W3214356764 modified "2023-09-27" @default.
- W3214356764 title "Eigenvalue ratios for vibrating String equations with concave densities" @default.
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