Related papers: On spectrum of strings with $\delta'$-like perturb…

This work investigates spectrum and root functions (that is, eigen- and associated functions) of a Sturm-Liouville problem involving an abstract linear operator (nonselfadjoint in general) in the equation together with supplementary…

The self-adjoint matrix Sturm-Liouville operator on a finite interval with a boundary condition in the general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the considered operator. These…

We apply both the theory of boundary triples and perturbation theory to the setting of semi-bounded Sturm-Liouville operators with two limit-circle endpoints. For general boundary conditions we obtain refined and new results about their…

We study the behavior of the limit of the spectrum of a non self-adjoint Sturm-Liouville operator with analytic potential as the semi-classical parameter $h\to 0$. We get a good description of the spectrum and limit spectrum near $\infty$.…

We present a complete description on the spectrum and eigenfunctions of the following two point boundary value problem $$(p(x)f')'-(q(x)-\lambda r(x))f=0\;, \;\; 0<x<L \quad ; \quad f'(0)=(\alpha_{1} \lambda + \alpha_{2}) f(0) \quad ; \quad…

We examine the spectrum of a family of Sturm--Liouville operators with regularly spaced delta function potentials parametrized by increasing strength. The limiting behavior of the eigenvalues under this spectral flow was described in a…

Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating properties of the eigenfunctions are studied. The spectral…

We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…

We study the asymptotic behaviour of eigenvalues and eigenfunctions of 2D vibrating systems with mass density perturbed in a vicinity of closed curves. The threshold case in which resonance frequencies of the membrane and thin inclusion…

We consider the linear eigenvalue problem \tag{1} -u" = \lambda u, \quad \text{on $(-1,1)$}, where $\lambda \in \mathbb{R}$, together with the general multi-point boundary conditions \tag{2} \alpha_0^\pm u(\pm 1) + \beta_0^\pm u'(\pm 1) =…

The paper deals with the Neumann spectral problem for a singularly perturbed second order elliptic operator with bounded lower order terms. The main goal is to provide a refined description of the limit behaviour of the principal eigenvalue…

In this paper, by using the similar methods of [O. Sh. Mukhtarov and M. Kadakal, Some spectral properties of one Sturm-Liouville type problem with discontinuous weight, Siberian Mathematical Journal, 46 (2005) 681-694] we extend some…

We study singular Sturm-Liouville operators of the form \[ \frac{1}{r_j}\left(-\frac{\mathrm d}{\mathrm dx}p_j\frac{\mathrm d}{\mathrm dx}+q_j\right),\qquad j=0,1, \] in $L^2((a,b);r_j)$, where, in contrast to the usual assumptions, the…

We consider the nonlinear equation $$-u'' = f(u) + h , \quad \text{on} \quad (-1,1),$$ where $f : {\mathbb R} \to {\mathbb R}$ and $h : [-1,1] \to {\mathbb R}$ are continuous, together with general Sturm-Liouville type, multi-point boundary…

In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov, Sturm-Liouville problems with discontinuities at two points, Comput. Math. Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary value problems…

In this work we investigate the resolvent operator and completeness of eigenfunctions of a Sturm-Liouville problem with discontinuities at two points. The problem contains an eigenparameter in the one of boundary conditions. For…

In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas…

We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures for diagonally dominant $J$-self-adjoint operator matrices. These are used in the proof of the central result, a perturbation…

This paper studies a Sturm--Liouville boundary value problem in which one of the boundary conditions depends bilinearly on the spectral parameter. The differential equation is considered on the interval $(0,1)$ with a classical boundary…

Spectral asymptotics of the Sturm-Liouville problem with a singular self-conformal weight measure is considered. A stronger version of the bounded distortion property is assumed for the conformal iterated function system corresponding to…