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In this paper, we prove the optimal upper bound λn λm ≤ ( n m )2 of vibrating string −y = λρ(x)y, with Dirichlet boundary conditions for single-well densities. The… Click to show full abstract
In this paper, we prove the optimal upper bound λn λm ≤ ( n m )2 of vibrating string −y = λρ(x)y, with Dirichlet boundary conditions for single-well densities. The proof is based on the inequality λn(ρ) λm(ρ) ≤ λn(L) λm(L) , with L must be a stepfunction. We also prove the same result for the Dirichlet Sturm-Liouville problems. 2000 Mathematics Subject Classification. Primary 34L15, 34B24.
Keywords:
vibrating string;
eigenvalue ratios;
ratios vibrating;
single well;
well densities;
string equations
Journal Title: Journal of Differential Equations
Year Published: 2022
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Journal Title: Journal of Differential Equations
Year Published: 2022
Link to full text (if available)
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recommendations!