Related papers: Dependence of Discrete Sturm-Liouville Eigenvalues…
We introduce a new biharmonic Steklov problem on differential forms with Dirichlet-type boundary conditions and show that it is elliptic. We prove the existence of a discrete spectrum for this problem and give variational characterizations…
The aim of this note is to study the spectrum of a linearized Liouville-type problem, characterizing the case in which the first eigenvalue is zero. Interestingly enough, we obtain also point-wise information on the associated first…
The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or…
This work provide a thorough study of L\'evy or heavy-tailed random matrices (LM). By analysing the self-consistent equation on the probability distribution of the diagonal elements of the resolvent we establish the equation determining the…
Taking advantage from the so-called "Lemma on small eigenvalues" by Colin de Verdi\`ere, we study ramification for multiple eigenvalues of the Dirichlet Laplacian in bounded perforated domains. The asymptotic behavior of multiple…
We study the characterization of several distance problems for linear differential-algebraic systems with dissipative Hamiltonian structure. Since all models are only approximations of reality and data are always inaccurate, it is an…
In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…
We show that there is no classical regular Sturm-Liouville problem on a finite interval whose spectrum consists of infinitely many distinct primes numbers. In particular, this answers in the negative a question raised by Zettl in his book…
We introduce a new class of Sturm-Liouville operators with periodically modulated parameters. Their spectral properties depend on the monodromy matrix of the underlying periodic problem computed for the spectral parameter equal to $0$.…
In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non…
The present paper shows that the eigenvalue sequence $\{\lambda_n(q)\}_{n\geqslant 1}$ of regular Sturm-Liouville eigenvalue problem with certain monotonic weights is uniformly Lipschitz continuous with respect to the potential $q$ on any…
The continuous dependence of solutions to certain (non-autonomous, partial, integro-differential-algebraic, evolutionary) equations on the coefficients is addressed. We give criteria that guarantee that convergence of the coefficients in…
In this paper we will explore fundamental constraints on the evolution of certain symplectic subvolumes possessed by any Hamiltonian phase space. This research has direct application to optimal control and control of conservative mechanical…
We are interested in the spectrum of the Dirichlet Laplacian in thin broken strips with angle $\alpha$. Playing with symmetries, this leads us to investigate spectral problems for the Laplace operator with mixed boundary conditions in…
The classical Liouville theorem states that a bounded harmonic function on all of $\RR^n$ must be constant. In the early 1970s, S.T. Yau vastly generalized this, showing that it holds for manifolds with nonnegative Ricci curvature.…
Eigenvalues of stochastic matrices have been studied from two complementary perspectives. The individual eigenvalues are characterised through the well-established Karpelevich regions. The spectrum as a whole has also been analysed,…
In this article we will explore Dirichlet Laplace eigenvalues on balls on spherically symmetric manifolds. We will compare any Dirichlet Laplace eigenvalue with the corresponding Dirichlet Laplace eigenvalue on balls in Euclidean space with…
We consider a Sturm-Liouville equation $\ell y:=-y'' + qy = \lambda y$ on the intervals $(-a,0)$ and $(0,b)$ with $a,b>0$ and $q \in L^2(-a,b)$. We impose boundary conditions $y(-a)\cos\alpha = y'(-a)\sin\alpha$, $y(b)\cos\beta =…
In Euclidean plane geometry, cycloids are curves which are homothetic to their respective bi-evolutes. In smooth normed planes, cycloids can be similarly defined, and they are characterized by their radius of curvature functions being…
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…