Related papers: Eigenvalue problems for Fredholm operators with se…

We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the…

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,…

Systems of linear ordinary differential equations with the most general inhomogeneous boundary conditions in fractional Sobolev spaces on a finite interval are studied. The Fredholm property of such problems in corresponding pairs of Banach…

We consider the Fredholm one-dimensional boundary-value problems in Sobolev spaces.We have obtained several important results about the indixes of functional operators, the criterion of their correct well-posedness, the criterion of the…

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,…

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…

The aim of this paper is to study the existence of eigenvalues in the gap of the essential spectrum of the one-dimensional Dirac operator in the presence of a bounded potential. We employ a generalized variational principle to prove…

We consider generalized operator eigenvalue problems in variational form with random perturbations in the bilinear forms. This setting is motivated by variational forms of partial differential equations with random input data. The…

We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…

Many physical systems can be described by nonlinear eigenvalues and bifurcation problems with a linear part that is non-selfadjoint e.g. due to the presence of loss and gain. The balance of these effects is reflected in an antilinear…

We prove that a linear fractional operator with an asymptotically constant lower order term in the whole space admits eigenvalues.

We prove necessary conditions for Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. These conditions are formulated in terms of indices of submultiplicative functions…

Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. In this paper, we consider the eigenvalue approximation of compact operators whose…

Muraleetharan and Thirulogasanthan in (J. Math. phys. 59, No. 10, 103506, 27p. (2018)) introduced the concept of Calkin Sspectrum of a bounded quaternionic linear operators. The study of this spectrum is establisched using the Fredholm…

We prove that a first order linear differential operator G with unbounded operator coefficients is Fredholm on spaces of functions on the real line with values in a reflexive Banach space if and only if the corresponding strongly continuous…

This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and…

We establish a Fredholm criterion for an arbitrary operator in the Banach algebra of singular integral operators with piecewise continuous coefficients on Nakano spaces (generalized Lebesgue spaces with variable exponent) with Khvedelidze…

We extend bifurcation results of nonlinear eigenvalue problems from real Banach spaces to any neighbourhood of a given point. For points of odd multiplicity on these restricted domains, we establish that the component of solutions through…

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate…

We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…