Related papers: Hartogs extension for systems of differential equa…
We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…
In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…
For a second-order linear differential equation with two irregular singular points of rank three, multiple Laplace-type contour integral solutions are considered. An explicit formula in terms of the Stokes multipliers is derived for the…
The majority of extensions to General Relativity display mathematical pathologies (higher derivatives, character change in equations that can be classified within PDE theory, and even unclassifiable ones) that cause severe difficulties to…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…
We consider a linear meromorphic system in the Birkhoff standard form. The construction of the isomonodromic deformation of it proposed by Bolibruch is discussed. This construction has some special characteristics because of resonant…
In this paper we shall study differential equations in the complex domain. The method of indeterminate coefficients and the majorant method lead to a proof of the existence and uniqueness of meromorphic solution of differential equations.…
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Pad\'{e} approximation and interpolation problems. We study also…
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
We extend Painlev\'e's determinateness theorem from the theory of ordinary differential equations in the complex domain allowing more general 'multiple-valued' Cauchy's problems. We study $C^0-$continuability (near singularities) of…
Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete…
Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow,…
We consider a non-autonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
A generalized KdV equation is formulated as an exterior differential system, which is used to determine the prolongation structure of the equation. The prolongation structure is obtained for several cases of the variable powers, and…
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
We provide a framework for studying the expansion rate of the image of a bounded set under a flow in Euclidean space and apply it to stochastic differential equations (SDEs for short) with singular coefficients. If the singular drift of the…