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

نویسندگانSeyfollah Mosazadeh
نشریهJournal of Pseudo-Differential Operators and Applications
ارائه به نام دانشگاهدانشگاه کاشان
شماره صفحات1-16
نوع مقالهFull Paper
تاریخ انتشار2020-07-02
رتبه نشریهISI
نوع نشریهالکترونیکی
کشور محل چاپسوئیس
نمایه نشریهSpringer

چکیده مقاله

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.
 

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