The equiconvergence of expansions in eigenfunctions and associated functions of an integral operator with involution

2008 ◽  
Vol 52 (5) ◽  
pp. 58-66
Author(s):  
L. P. Kuvardina ◽  
A. P. Khromov
Keyword(s):  
Integral Operator ◽  
Associated Functions ◽  
Eigenfunctions And Associated Functions

scholarly journals On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
N. S. Imanbaev
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Basis Property ◽  
Differentiation Operator ◽  
Stability And Instability ◽  
Associated Functions ◽  
Sturm Liouville ◽  
Type Boundary ◽  
Eigenfunctions And Associated Functions ◽  
Integral Perturbation

We study a question on stability and instability of basis property of system of eigenfunctions and associated functions of the double differentiation operator with an integral perturbation of Samarskii-Ionkin type boundary conditions.

Bifurcation of Eigenvalues of Nonselfadjoint Differential Operators in Nonconservative Stability Problems

2002 ◽  
Author(s):  
Oleg N. Kirillov ◽  
Alexander P. Seyranian
Keyword(s):  
Parameter Space ◽  
Differential Operators ◽  
Eigenvalue Problems ◽  
Initial Point ◽  
Potential Force ◽  
Arbitrary Length ◽  
Eigen Values ◽  
Associated Functions ◽  
Linear Differential ◽  
Eigenfunctions And Associated Functions

In the present paper eigenvalue problems for non-selfadjoint linear differential operators smoothly dependent on a vector of real parameters are considered. Bifurcation of eigenvalues along smooth curves in the parameter space is studied. The case of multipleeigen value with Keldysh chain of arbitrary length is considered. Explicit expressions describing bifurcation of eigen-values are found. The obtained formulae use eigenfunctions and associated functions of the adjoint eigenvalue problems as well as the derivatives of the differential operator taken at the initial point of the parameter space. These results are important for the stability theory, sensitivity analysis and structural optimization. As a mechanical application the extended Beck’s problem of stability of an elastic column under action of potential force and tangential follower force is considered and discussed in detail.

scholarly journals Solving the Boundary Value Problems for Differential Equations with Fractional Derivatives by the Method of Separation of Variables

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1877
Author(s):  
Temirkhan Aleroev
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Derivatives ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Fourier Method ◽  
Associated Functions ◽  
Sturm Liouville ◽  
Eigenfunctions And Associated Functions ◽  
Adjoint Operators

This paper is devoted to solving boundary value problems for differential equations with fractional derivatives by the Fourier method. The necessary information is given (in particular, theorems on the completeness of the eigenfunctions and associated functions, multiplicity of eigenvalues, and questions of the localization of root functions and eigenvalues are discussed) from the spectral theory of non-self-adjoint operators generated by differential equations with fractional derivatives and boundary conditions of the Sturm–Liouville type, obtained by the author during implementation of the method of separation of variables (Fourier). Solutions of boundary value problems for a fractional diffusion equation and wave equation with a fractional derivative are presented with respect to a spatial variable.

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