Eigenvalue distribution of some fractal semi-elliptic differential operators

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.

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

On the principal eigenvalue of elliptic operators in R and applications

Two generalizations of the notion of principal eigenvalue for elliptic operators in RN are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semi-linear problems in all of space. We a...

The conditioning of FD matrix sequences coming from semi-elliptic differential equations

In this paper we are concerned with the study of spectral properties of the sequence of matrices {An(a)} coming from the discretization, using centered finite differences of minimal order, of elliptic (or semielliptic) differential operators L(a, u) of the form { − d dx ( a(x) d dx u(x) ) = f (x) on = (0, 1), Dirichlet B.C. on , (1) where the nonnegative, bounded coefficient function a(x) of th...