On an inverse spectral problem for Sturm - Liouville operator with discontinuous coefficient

Abstract

In this work, a boundary value problem for Sturm-Liouville operator with discontinuous coefficient is examined. The main equation is obtained which has an important role in solution of inverse problem for boundary value problem and uniqueness of its solution is proved. Uniqueness theorem for the solution of the inverse problem is given.2010 Mathematics Subject Classification. 34A55; 34K10.

Finding the condition of finiteness of the discrete spectrum of a nonself-adjoint friedrichs model in the case of one-dimensional perturbation

“…Це можна застосувати до різних фізичних задач, використовуючи позитивно визначені оператори моделі Фрідріхса без їх спектрального розкладу та рівності Парсевала. У роботі [3] досліджено пряму та обернену задачу для оператора Штурма-Ліувілля, вивчено його спектральні особливості та встановлена ортогональність власних функцій та власні значення. Розглянуто асимптотичну формулу власних значень та власних функцій оператора Штурма-Ліувілля та отримано спектральний розклад.…”

Construction of spectral decomposition for non-self-adjoint friedrichs model operator

“…In this paper, these results are obtained for a finite gap ( , ), 0 p that is, this refers to the space L 2 0 ( , ). p The problem of localization of spectral singularities of dissipative operators in terms of the asymptotics of the corresponding exponential function is considered in [12] and the solution of this problem for the spectral singularities of higher orders is presented. We study the Weyl function for the perturbed Laplacian in space L R 2 3 ( ) , using a traditional classi cal approach.…”

“…By using the analytic prolongation and changing the symbols ν ζ → ∈Ω, m → ∈ z Ω, we obtain the equality (11) from (12).…”

Impulsive Sturm-Liouville Problems on Time Scales

“…Impulsive differential equations have recently been subject to an increasing number of investigations since they occur in mathematical modeling of various areas of science, e.g., population dynamics, economics, optimal control, and chemotherapy. These equations have been studied by several authors (see [3,9,16,17,18,21] ).…”