On manifolds of eigenfunctions and potentials generated by a family of periodic boundary-value problems

  • Ya. M. Dymarskii Луган. гос. ун-т внутренних дел им. Э. А. Дидоренко

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.
Published
25.06.1996
How to Cite
DymarskiiY. M. “On Manifolds of Eigenfunctions and Potentials Generated by a Family of Periodic Boundary-Value Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 48, no. 6, June 1996, pp. 771-8, https://umj.imath.kiev.ua/index.php/umj/article/view/5277.
Section
Research articles