Related papers: On calculation of eigenvalues of Sturm-Liouville p…
In this paper we consider the Sturm-Liouville equation -y"+qy = lambda*y on the half line (0,infinity) under the assumptions that x=0 is a regular singular point and nonoscillatory for all real lambda, and that either (i) q is L_1 near…
In this paper we are concerned with a new class of BVP' s consisting of eigendependent boundary conditions and two supplementary transmission conditions at one interior point. By modifying some techniques of classical Sturm-Liouville theory…
Regular Sturm-Liouville problems with indefinite weight functions may possess finitely many non-real eigenvalues. In this note we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the…
We study a Sturm-Liouville type eigenvalue problem for second-order differential equations on the infinite interval. Here the eigenfunctions are nonzero solutions exponentially decaying at infinity. We prove that at any discrete eigenvalue…
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…
In this paper we consider generalized eigenvalue problems for a family of operators with a quadratic dependence on a complex parameter. Our model is $L(\lambda)=-\triangle +(P(x)-\lambda)^2$ in $L^2(\R^d)$ where $P$ is a positive elliptic…
We investigate the following eigenvalue problem \begin{align*} \begin{cases} -\operatorname{div}\left( L(x) |\nabla u| ^{p-2}\nabla u\right)=\lambda K(x)|u|^{p-2}u \quad \text{in } A_{R_1}^{R_2} , u=0\quad \text{on } \partial A_{R_1}^{R_2}…
A novel method for finding the eigenvalues of a Sturm-Liouville problem is developed. Following the minimalist approach the problem is transformed to a single first-order differential equation with appropriate boundary conditions. Although…
In the present review we deal with the recently introduced method of spectral parameter power series (SPPS) and show how its application leads to an explicit form of the characteristic equation for different eigenvalue problems involving…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
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…
For a particular family of long-range potentials $V$, we prove that the eigenvalues of the indefinite Sturm--Liouville operator $A = \mathrm{sign}(x)(-\Delta + V(x))$ accumulate to zero asymptotically along specific curves in the complex…
The present paper gives a priori bounds on the possible non-real eigenvalues of regular indefinite Sturm-Liouville problems and obtains sufficient conditions for such problems to admit non-real eigenvalues.
We calculate eigenvalues of one-dimensional quantum-systems by the exact numerical solution of the Lippmann-Schwinger equation, analogous to the scattering problem. To illustrate our method, we treat elementary problems: the harmonic and…
We derive eigenvalue asymptotics for Sturm--Liouville operators with singular complex-valued potentials from the space $W^{\al-1}_{2}(0,1)$, $\al\in[0,1]$, and Dirichlet or Neumann--Dirichlet boundary conditions. We also give application of…
We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires…
The eigenvalue problem on the circle for the non-self-adjoint operators $L_{m}(V)=(-1)^{m}\frac{d^{2m}}{dx^{2m}}+V$, $m\in \mathbb{N}$ with singular complex-valued 2-periodic distributions $V\in H_{per}^{-m}[-1,1]$ is studied. Asymptotic…
Inverse problems of recovering the coefficients of Sturm-Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2)…
In this paper, we shall derive a spectral matrix method for the approximation of the eigenvalues of (weakly) regular and singular Sturm-Liouville problems in normal form with an unbounded potential at the left endpoint. The method is…
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…