Related papers: Comparison results for first order linear operator…
We develop Weyl-Titchmarsh theory for self-adjoint Schr\"odinger operators $H_{\alpha}$ in $L^2((a,b);dx;\cH)$ associated with the operator-valued differential expression $\tau =-(d^2/dx^2)+V(\cdot)$, with $V:(a,b)\to\cB(\cH)$, and $\cH$ a…
We consider a "superposition operator" obtained through the continuous superposition of operators of mixed fractional order, modulated by a signed Borel finite measure defined over the set $[0, 1]$. The relevance of this operator is rooted…
We consider a problem of finding vanishing at infinity $C^1([0,\oo))$-solutions to non-homogeneous system of linear ODEs which has the pole of first order at $x=0$. The resonant case where the corresponding homogeneous problem has…
Eigenvalue problems arise in many areas of physics, from solving a classical electromagnetic problem to calculating the quantum bound states of the hydrogen atom. In textbooks, eigenvalue problems are defined for linear problems,…
Singular Green operators G appear typically as boundary correction terms in resolvents for elliptic boundary value problems on a domain \Omega \subset R^n, and more generally they appear in the calculus of pseudodifferential boundary…
The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting…
Recent work in the literature has studied fourth-order elliptic operators on manifolds with boundary. This paper proves that, in the case of the squared Laplace operator, the boundary conditions which require that the eigenfunctions and…
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…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
We find an asymptotic expression for the first eigenvalue of the biharmonic operator on a long thin rectangle. This is done by finding lower and upper bounds which become increasingly accurate with increasing length. The lower bound is…
The aim of this paper consists on the study of the following fourth-order operator: \begin{equation}\label{Ec::T4} T[M]\,u(t)\equiv u^{(4)}(t)+p_1(t)\,u"'(t)+p_2(t)\,u"(t)+M\,u(t)\,,\ t\in I \equiv [a,b]\,, \end{equation} coupled with the…
The paper is concerned with a sequence of constants which appear in several problems. These problems include the minimal eigenvalue of certain positive definite Toeplitz matrices, the minimal eigenvalue of some higher-order ordinary…
In this article we obtain two-sided estimates for the Greens function of fractional boundary value problems on $\mathbb R_+ \times \mathbb R_+ \times \mathbb R^d$ of the form \[(-{}_{t_1}D^\beta_{0+*} - {}_{t_2}D^\gamma_{0+*})u(t_1, t_2, x)…
We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…
The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied. We prove a well-posedeness of linear problem and optimal regularity result for the nonlinear problem which occur in fluid…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
The aim of this work is to study the existence of a periodic solutions of third order differential equations $z'''(t) = Az(t) + f(t)$ with the periodic condition $x(0) = x(2\pi), x'(0) = x'(2\pi)$ and $x''(0) = x''(2\pi)$. Our approach is…
We study the spectral theory of mixed local and nonlocal operators with lower-order terms in the right-hand side of the equation. This kind of problems is motivated by the analysis of superposition operators of mixed order and with the…
We consider an approximate solution for the one-dimensional semilinear singularly-perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of…
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) =…