Related papers: Eigenvalue problems for Fredholm operators with se…
This paper has aim to characterize Fredholmness and Weylness of upper triangular operator matrices having arbitrary dimension n. We present various characterization results in the setting of infinite dimensional Hilbert spaces, thus…
In this work, we revisit the Krein-Rutman theory for semigroups of positive operators in a Banach lattice framework and we provide some very general, efficient and handy results with constructive estimates about: the existence of a solution…
This article investigates the existence and uniqueness of solutions to the second order Volterra integrodifferential equations with nonlocal and boundary conditions through its integral equivalent equations and fixed point of Banach.…
When extending bifurcation theory of dynamical systems to nonautonomous problems, it is a central observation that hyperbolic equilibria persist as bounded entire solutions under small temporally varying perturbations. In this paper, we…
In this paper the boundary value problem for one class of the operator-differential equations of the third order on a semi-axis, where one of the boundary conditions is perturbed by some linear operator is researched. There are received…
The Riesz projection and the corresponding eigenfunction of a positive operator satisfying the Doeblin condition are explicitly constructed using the partial Bell polynomials. While classical Fredholm theory requires stringent summability…
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…
We investigate nonlinear eigenproblems for a broad class of proper, closed, convex functionals in reflexive Banach spaces. We develop a dual formulation of the nonlinear eigenproblem using the Fenchel conjugate and establish an equivalence…
We establish $C^{1,1}$-regularity and uniqueness of the first eigenfunction of the complex Hessian operator on strongly $m$-pseudoconvex manifolds, along with a variational formula for the first eigenvalue. From these results, we derive a…
In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for…
We study real resonances and embedded eigenvalues of the Kramers--Fokker--Planck operator with a long-range potential. We prove that thresholds are only possible accumulation points of eigenvalues and that the limiting absorption principle…
In this paper, we investigate the unique solvability of a mixed boundary value problem for a fractional partial differential equation featuring a degenerate coefficient. By introducing a novel operator and applying the method of separation…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local. We show the…
We show that some previous results concerning the boundedness of differentiation and integration operators on weighted spaces given by radial weights in the unit disk or the complex plane might fail without some natural additional…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral…
Recently, the eigenvalue problems formulated with symmetric positive definite bilinear forms have been well investigated with the aim of explicit bounds for the eigenvalues. In this paper, the existing theorems for bounding eigenvalues are…
We discuss, via a version of the Birkhoff-Kellogg theorem, the existence of positive and negative eigenvalues of Hammerstein integral equations with sign-changing nonlinearities and functional terms. The corresponding eigenfunctions have a…
We develop a general approach to virtual levels in Banach spaces. We show that virtual levels admit several characterizations which are essentially equivalent: (1) there are corresponding virtual states (from a certain larger space); (2)…