An inverse spectral problem for a nonsymmetric differential operator: Reconstruction of eigenvalue problem

An inverse spectral problem for a nonsymmetric differential operator: Uniqueness and reconstruction formula

We consider an eigenvalue problem for a system in [0, 1]:        0 1 1 0 d dx + p11(x) p12(x) p21(x) p22(x) ϕ (1) (x) ϕ (2) (x) = λ ϕ (1) (x) ϕ (2) (x) ϕ (2) (0) cosh µ − ϕ (1) (0) sinh µ = ϕ (2) (1) cosh ν + ϕ (1) (1) sinh ν = 0 with constants µ, ν ∈ C. Under the assumption that p21, p22 are known, we prove a uniqueness theorem and provide a reconstruction formula for p11 and p12 from t...

On stability of an inverse spectral problem for a nonsymmetric differential operator

In this paper, we consider the stability of an inverse spectral problem for a nonsymmetric ordinary differential operator. We give an estimate for deviation in the coefficients of this operator when the spectral data perturb. Our result shows that if two spectral data are sufficiently close to one another, then the corresponding two differential operators must be close each other in the sense o...

On an Inverse Eigenvalue Problem for a Semilinear Sturmäliouville Operator

Inverse problem for a singular differential operator

In this paper, we give the solution of the inverse Sturm–Liouville problem on two partially coinciding spectra. In particular, in this case we obtain Hochstadt's theorem concerning the structure of the difference q(x) − ˜ q(x) for the singular Sturm Liouville problem defined on the finite interval (0, π) having the singularity type 1 4 sin 2 x at the points 0 and π.

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...