The Eigenvalues of a Class of Elliptic Differential Operators

Transmission Eigenvalues for Elliptic Operators

A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trac...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Enclosure Theorems for Eigenvalues of Elliptic Operators

are to be considered when the coefficients a,-,-, b, and c are continuous real-valued functions with &=^0, c>0 in En. The ellipticity of L implies that the symmetric matrix (a,,) is everywhere positive definite. A "solution" u of Lu = 0 is supposed to be of class C1 and all derivatives involved in (1.1) are supposed to exist, be continuous, and satisfy Lu = 0 at every point. The eigenvalue prob...

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...

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.