A new approach to asymptotic formulas for eigenfunctions of discontinuous non-selfadjoint Sturm–Liouville operators

AuthorsSeyfollah Mosazadeh
JournalJournal of Pseudo-Differential Operators and Applications
Presented byUniversity of Kashan
Page number1-16
Paper TypeFull Paper
Published At2020-07-02
Journal GradeISI
Journal TypeElectronic
Journal CountrySwitzerland
Journal IndexSpringer

Abstract

In the present paper, boundary value problems for discontinuous non-selfadjoint Sturm–Liouville operators on a finite interval with boundary conditions nonlinearly dependent on the spectral parameter are considered, and a new approach for studying the asymptotic representation of the eigenfunctions and their partial derivatives is presented. We obtain the asymptotic representation of the solutions and the eigenvalue, and study some of their main properties. Then, we provide a constructive procedure to obtain the asymptotic form of the eigenfunctions and their partial derivatives in discontinuous case by the canonical form of the Bessel functions J_1/2(z), J_3/2(z) and their derivatives.
 

Paper URL