Abstract
We consider a family of boundary-value problems with some potential as a parameter. We study the manifold of normalized eigenfunctions with even number of zeros in a period, and the manifold of potentials associated with double eigenvalues. In particular, we prove that the manifold of normalized eigenfunctions is a trivial fiber space over a unit circle and that the manifold of potentials with double eigenvalues is a homotopically trivial manifold trivially imbedded into the space of potentials.
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Dymarskii, Y.M. On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems. Ukr Math J 48, 866–879 (1996). https://doi.org/10.1007/BF02384172
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DOI: https://doi.org/10.1007/BF02384172