Related papers: Asymptotic formulas for eigenvalues and eigenfunct…
In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to…
We study invariance for eigenvalues of families of selfadjoint Sturm-Liouville operators with local point interactions. In a probabilistic setting, we show that a point is either an eigenvalue for all members of the family or only for a set…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. Especially, Neumann and Robin BVPs are considered. The main obstacle for applying the usual…
For integers $m\geq 3$, we study the non-self-adjoint eigenvalue problems $-u^{\prime\prime}(x)+(x^m+P(x))u(x)=E u(x)$, $0\leq x<+\infty$, with the boundary conditions $u(+\infty)=0$ and $\alpha u(0)+\beta u^{\prime}(0)=0$ for some $\alpha,…
We obtain asymptotic representations as $\lambda \to \infty$ in the upper and lower half-planes for the solutions of the Sturm--Liouville equation $$ -y"+p(x)y'+q(x)y= \lambda ^2 \rho(x)y, \qquad x\in [a,b] \subset \mathbb{R}, $$ under the…
On the basis of the theory of Sturm--Liouville problem with distribution coefficients we get the infima and suprema of the first eigenvalue of the problem $-y" + (q-\lambda) y=0, y'(0) -k_0^2 y(0) = y'(1) + k_1^2 y(1) = 0$, where $q$…
We report a new analytical method for solution of a wide class of second-order differential equations with eigenvalues replaced by arbitrary functions. Such classes of problems occur frequently in Quantum Mechanics and Optics. This approach…
This paper provides results for eigencurves associated with self-adjoint linear elliptic boundary value problems. The elliptic problems are treated as a general two-parameter eigenproblem for a triple (a, b, m) of continuous symmetric…
Sturm-Liouville problems are abundant in the numerical treatment of scientific and engineering problems. In the present contribution, we present an efficient and highly accurate method for computing eigenvalues of singular Sturm-Liouville…
The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…
We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori…
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…
In this paper, we study the eigenvalue problem of stochastic Hamiltonian system driven by Brownian motion and Markov chain with boundary conditions and time-dependent coefficients. For any dimensional case, the existence of the first…
In this paper we study a Sturm--Liouville operator $Ly=-y"+q(x)y$ in the space $L_2[0,\pi]$ with Direchlet boundary conditions. Here the potential $q$ is a first order distribution: $q\in W_2^{-1}[0,\pi]$. Such operators were defined in our…
The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…
In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem supplemented with nonlocal Riemann-Liouville fractional integral and Caputo fractional derivative boundary conditions. Our…
This paper is concerned with eigenvalue problems for non-symmetric elliptic operators with large drifts in bounded domains under Dirichlet boundary conditions. We consider the minimal principal eigenvalue and the related principal…
We show that all self-adjoint extensions of semi-bounded Sturm--Liouville operators with general limit-circle endpoint(s) can be obtained via an additive singular form bounded self-adjoint perturbation of rank equal to the deficiency…
A class of (1+1)--dimensional nonlinear boundary value problems (BVPs), modeling the process of melting and evaporation of solid materials, is studied by means of the classical Lie symmetry method. New definition of invariance in Lie's…