Special Session 156: Structure and dynamics of solutions for nonlinear elliptic and parabolic equations

The Lam`e equation on the circle and applications to singular limite eigenvalue problems
Toru Wakasa
Kyushu Institute of Technology
Japan
Co-Author(s):    Yasuhito Miyamoto, Kouichi Takemura
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.