| Abstract: |
| We study a kind of reverse spectral problems for Camassa-Holm equations. The aim is to prove the explicit solutions for the extremal $L^1$-norms of the potentials, given the first fixed periodic eigenvalue or any fixed Dirichlet eigenvalue. We use the setting of measure differential equations to understand such problems
because the solution will lead to Dirac measure distributions of potentials. The explicit expressions for the sharp bounds are given as some elementary functions. |
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