Related papers: On a differential operator with absent spectrum

We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…

For a class of zero order pseudodifferential operators we find the asymptotics of eigenvalues converging to a non-isolated tip of the essential spectrum.

This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…

In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…

The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied. We prove a well-posedeness of linear problem and optimal regularity result for the nonlinear problem which occur in fluid…

We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The…

We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…

In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…

For one boundary problem of fourth order with a spectral parameter in the boundary condition we prove the simplicity of the spectrum and the oscillation properties of the system of the eigenfunctions derivatives.

In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…

I revisit the so called "bispectral problem" introduced in a joint paper with Hans Duistermaat a long time ago, allowing now for the differential operators to have matrix coefficients and for the eigenfunctions, and one of the eigenvalues,…

We suggest a modification of the operator exponential method for the numerical solving the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions…

In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…

The paper develops a theory of spectral boundary value problems from the perspective of general theory of linear operators in Hilbert spaces. An abstract form of spectral boundary value problem with generalized boundary conditions is…

In this paper we study the spectrum of a fundamental differential operator on a Hilbert-P\'olya space. A number is an eigenvalue of this differential operator if and only if it is a nontrivial zero of the Riemann zeta function. An explicit…

In this paper, we study the spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions subject to Dirichlet type, Neumann type and spatial periodic type boundary conditions. We first obtain necessary and…

The paper is pertaining to the spectral theory of operators and boundary value problems for differential equations on manifolds. Eigenvalues of such problems are studied as functionals on the space of domains. Resolvent continuity of the…

This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the…

In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.

Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…