Displaying similar documents to “Basis properties of eigenfunctions of nonlinear Sturm-Liouville problems.”

On the basis property of the root functions of differential operators with matrix coefficients

Oktay Veliev (2011)

Open Mathematics

Similarity:

We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.

Spectral properties of some regular boundary value problems for fourth order differential operators

Nazim Kerimov, Ufuk Kaya (2013)

Open Mathematics

Similarity:

In this paper we consider the problem y i v + p 2 ( x ) y ' ' + p 1 ( x ) y ' + p 0 ( x ) y = λ y , 0 < x < 1 , y ( s ) ( 1 ) - ( - 1 ) σ y ( s ) ( 0 ) + ∑ l = 0 s - 1 α s , l y ( l ) ( 0 ) = 0 , s = 1 , 2 , 3 , y ( 1 ) - ( - 1 ) σ y ( 0 ) = 0 , where λ is a spectral parameter; p j (x) ∈ L 1(0, 1), j = 0, 1, 2, are complex-valued functions; α s;l, s = 1, 2, 3, l = 0 , s - 1 ¯ , are arbitrary complex constants; and σ = 0, 1. The boundary conditions of this problem are regular, but not strongly regular. Asymptotic formulae for eigenvalues and eigenfunctions of the considered boundary value problem are established in the case α 3,2 + α 1,0 ≠ α 2,1. It is proved that the system of root functions of this...

Stabilization of Timoshenko Beam by Means of Pointwise Controls

Gen-Qi Xu, Siu Pang Yung (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build...