Pekeris Substitution and Some Spectral Properties of the Rayleigh Boundary Value Problem

2013 ◽  
pp. 63-69 ◽  
Author(s):  
V. M. Markushevich
Keyword(s):  
Boundary Value Problem ◽  
Spectral Properties ◽  
Boundary Value

On the spectral properties and positivity of solutionsof a periodic boundary value problemfor a second-order functional differential equation

2020 ◽  
pp. 123-130
Author(s):  
Manuel J. Alves ◽  
Sergey M. Labovskiy
Keyword(s):  
Differential Equation ◽  
Green Function ◽  
Differential Operator ◽  
Boundary Value Problem ◽  
Functional Differential Equation ◽  
Spectral Properties ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Functional Differential ◽  
The Green Function

For a functional-differential operator Lu = (1/ρ)(-(pu')' + ∫_0^l▒〖u(s)d_s r(x,s)〗) with symmetry, the completeness and orthogonality of the eigenfunctions is shown. Thepositivity conditions of the Green function of the periodic boundary value problem areobtained.

scholarly journals Spectral analysis of Hahn-Dirac system

2021 ◽  
Author(s):  
Bilender Allahverdiev ◽  
Hüseyin Tuna
Keyword(s):  
Spectral Analysis ◽  
Boundary Value Problem ◽  
Spectral Properties ◽  
Orthonormal Basis ◽  
Boundary Value ◽  
Dirac System ◽  
One Dimensional ◽  
Countable Sequence ◽  
Greens Function ◽  
The One

In this paper, we study some spectral properties of the one-dimensional Hahn-Dirac boundary-value problem, such as formally self-adjointness, the case that the eigenvalues are real, orthogonality of eigenfunctions, Greens function, the existence of a countable sequence of eigenvalues, eigenfunctions forming an orthonormal basis of L2w,q ((w0. a): E).

scholarly journals Spectral Properties of Nonhomogenous Differential Equations with Spectral Parameter in the Boundary Condition

2014 ◽  
Vol 22 (2) ◽  
pp. 109-120
Author(s):  
Özkan Karaman
Keyword(s):  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Analytic Functions ◽  
Spectral Properties ◽  
Boundary Value ◽  
Uniqueness Theorems ◽  
Spectral Singularities ◽  
Boundary Properties ◽  
Boundary Uniqueness ◽  
Complex Valued

AbstractIn this paper, using the boundary properties of the analytic functions we investigate the structure of the discrete spectrum of the boundary value problem (0.1)$$\matrix{\hfill {iy_1^\prime + q_1 \left(x \right)y_2 - \lambda y_1 = \varphi _1 \left(x \right)\;\;} & \hfill {} \cr \hfill {- iy_2^\prime + q_2 \left(x \right)y_1 - \lambda y_2 = \varphi _2 \left(x \right),} & \hfill {x \in R_ + } \cr }$$ and the condition (0.2)$$\left({a_1 \lambda + b_1 } \right)y_2 \left({0,\lambda } \right) - \left({a_2 \lambda + b_2 } \right)y_1 \left({0,\lambda } \right) = 0$$ where q1,q2, φ1, φ2 are complex valued functions, ak ≠ 0, bk ≠ 0, k = 1, 2 are complex constants and λ is a spectral parameter. In this article, we investigate the spectral singularities and eigenvalues of (0.1), (0.2) using the boundary uniqueness theorems of analytic functions. In particular, we prove that the boundary value problem (0.1), (0.2) has a finite number of spectral singularities and eigenvalues with finite multiplicities under the conditions, $$\matrix{{\mathop {\sup }\limits_{x \in R_ + } \left[ {\left| {\varphi _k \left(x \right)} \right|\exp \left({\varepsilon x^\delta } \right)} \right] < \infty ,\;\;\;k = 1.2} \hfill \cr {\mathop {\sup }\limits_{x \in R_ + } \left[ {\left| {q_k \left(x \right)} \right|\exp \left({\varepsilon x^\delta } \right)} \right] < \infty ,\;\;\;k = 1.2} \hfill \cr }$$ for some ε > 0, ${1 \over 2} < \delta < 1$

scholarly journals ON SOME SPECTRAL PROPERTIES OF THIRD ORDER NONLINEAR BOUNDARY VALUE PROBLEMS

2012 ◽  
Vol 17 (1) ◽  
pp. 78-89 ◽  
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Value Problem ◽  
Spectral Properties ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Third Order ◽  
Number Of Solutions ◽  
Nodal Structure ◽  
The Third ◽  
Nonlinear Boundary Value

The present paper deals with a two point the third-order nonlinear boundary value problem. An estimation of the number of solutions to boundary value problem and their nodal structure are established. Some results are given on spectral properties of solutions.

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