Asymptotic behavior of the spectrum of a boundary-value problem with a spectral parameter in the boundary condition

1983 ◽  
Vol 34 (6) ◽  
pp. 638-643
Author(s):  
V. G. Palyutkin
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Boundary Value

scholarly journals A boundary value problem with a discontinuous coefficient and containing a spectral parameter in the boundary condition

1995 ◽  
Vol 18 (1) ◽  
pp. 133-140 ◽  
Author(s):  
A. A. Darwish
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Continuous Spectrum ◽  
Discrete Spectrum ◽  
Spectral Parameter ◽  
Boundary Value ◽  
Adjoint Problem ◽  
Discontinuous Coefficient ◽  
Eigenvalue Equation

A singular non-self-adjoint boundary value problem is considered. This problem has a discontinuous coefficient with a spectral parameter in the boundary condition. Some solutions of the eigenvalue equation are given. The discrete spectrum is studied and the resolvent is obtained. Formulation of the adjoint problem is deduced and hence the continuous spectrum of the considered problem is given. Furthermore, the spectrum of the adjoint problem is investigated.

scholarly journals Spectral Analysis of -Sturm-Liouville Problem with the Spectral Parameter in the Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Aytekin Eryılmaz
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Spectral Parameter ◽  
Difference Operator ◽  
Boundary Value ◽  
Liouville Problem ◽  
Scattering Matrix ◽  
Eigenvalues And Eigenvectors ◽  
Sturm Liouville ◽  
Spectral Representations

This paper is concerned with -Sturm-Liouville boundary value problem in the Hilbert space with a spectral parameter in the boundary condition. We construct a self-adjoint dilation of the maximal dissipative -difference operator and its incoming and outcoming spectral representations, which make it possible to determine the scattering matrix of the dilation. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of operator generated by boundary value problem.

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

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