Eigenfunction behavior and adaptive finite element approximations of nonlinear eigenvalue problems in quantum physics

In this paper, we investigate a class of nonlinear eigenvalue problems resulting from quantum physics. We first prove that for any open set G , there exists an eigenfunction cannot be polynomial on which may reviewed as refinement the classic unique continuation property. Then apply non-polynomial behavior to show adaptive finite element approximations are convergent even if initial mesh is not fine enough. finally remark similar arguments can applied linear improve relevant existing results.