Spectral Analysis of Higher-Order Differential Operators with Discontinuity Conditions at an Interior Point

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Lp SPECTRAL THEORY OF HIGHER-ORDER ELLIPTIC DIFFERENTIAL OPERATORS

a class of fourth order differential operators with transmission conditions

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...

On the spectral functions for the higher-order differential operators with trivial boundary conditions and regularized trace of perturbation operators of the first order

0.1 Definition. Let ly = (−1)y + p2m−2(x)y + p2m−3(x)y + · · · + p1(x)y + p0(x)y (1) be a differential expression with real coefficients pk(x). We study the self-adjoint extension 1 L2m p (I), (p = (p2m−2(x), p2m−3(x), . . . , p1(x), p0(x))) of the differential expression l(y) on I (I = R or R+ = [0; +∞)). This differential expression is defined on I with the boundary conditions y(0) = y′(0) = ...

Spectral Analysis for Differential Operators with Singularities

Nonselfadjoint boundary value problems for second-order differential equations on a finite interval with nonintegrable singularities inside the interval are considered under additional sewing conditions for solutions at the singular point. We study properties of the spectrum, prove the completeness of eigenand associated functions, and investigate the inverse problem of recovering the boundary ...