The initial aim of the present paper is to provide a complete description for the eigenvalue problem of the non-commutative harmonic oscillator (NcHO), which is given by a two-by-two system of paritypreserving ordinary differential operator [19], in terms of Heun’s ordinary differential equations, the second order Fuchsian differential equations with four regular singularities in a complex doma...

The following work is an extension of our recent paper 10]. We still deal with nonlinear eigenvalue problems of the form A 0 y + B(y)y = y (*) in a real Hilbert space H with a semi-bounded self-adjoint operator A 0 , while for every y from a dense subspace X of H, B(y) is a symmetric operator. The left{hand side is assumed to be related to a certain auxiliary functional , and the associated lin...

Convergence of an approximate method for determining vibrational eigenpairs of an elastic solid containing an incompressible fluid is examined. The field variables are solid displacement and fluid pressure. We show that in suitable Sobolev spaces a variational formulation exists whose solution eigenvalues and eigenfunctions are identified with those of a compact operator. A nonconforming finite...

Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

Let D ⊂ R be a bounded domain and let L = 1 2 ∇ · a∇+ b · ∇ be a second order elliptic operator on D. Let ν be a probability measure on D. Denote by L the differential operator whose domain is specified by the following non-local boundary condition: DL = {f ∈ C (D) : Z D fdν = f |∂D}, and which coincides with L on its domain. Clearly 0 is an eigenvalue for L, with the corresponding eigenfunctio...

This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be pre-calculated and thereby effectively reduces the complexity of the problem to a calculation over the surface. Several eigenvalues are retrieved simultaneously. ...

This study investigates some spectral properties of a new type periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that differential equation is given on two disjoint segments have common end, and additional interaction conditions are imposed this end (such called various names, including transmission conditions, jump interface impulsive etc.). A...

We report on a direct connection between quasi-periodic topology and the Almost Mathieu (Andre-Aubry) metal insulator transition (MIT). By constructing transfer matrix equations from limit of rational approximate projected Green's functions, we relate results $\text{SL}(2,\mathbb{R})$ co-cycle theory (transfer eigenvalue scaling) to consequences band theory. This reduction links eigenfunction l...

We consider a compact perturbation $H_0 = S + K_0^* K_0$ of self-adjoint operator $S$ with an eigenvalue $\lambda^\circ$ below its essential spectrum and the corresponding eigenfunction $f$. The is assumed to be "along" $f$, namely $K_0f=0$. belongs spectra both $H_0$ $S$. Let have $\sigma$ more eigenvalues than $H_0$; known as spectral shift at $\lambda^\circ$. now allow vary in suitable space...