| Abstract: |
| It is known that for the Lam`e equation appears in the linearized eigenvalue problems associated with the solutions of nonlinear ODEs.
The Lam`e potential is expressed in the Jacobi sn-functions, and it is interesting to consider the case the modulus k is close to 1, from the viewpoint of singular limit problems.
In this talk, we will show precise the asymptotic formula of all eigenvalues of Lam`e equations as k to 1 under the periodic boundary condition.
Moreover, the asymptotic results will be applied to several linearized eigenvalue problems. |
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