Related papers: A Grobman-Hartman theorem for a differential equat…
We study differentiability properties in a particular case of the Palmer's linearization Theorem, which states the existence of an homeomorphism $H$ between the solutions of a linear ODE system having exponential dichotomy and a quasilinear…
We investigate the differentiability of the conjugacy in a nonautonomous version of the Hartman--Grobman Theorem for systems with finite delay, where the linear part satisfies a $\mu$-dichotomy. Under suitable conditions on the nonlinear…
In this article we formulate and prove sufficient conditions for the existence of trajectories of nonstationary periodic solutions of autonomous Hamiltonian systems in a neighbourhood of equilibria. It is worth pointing out that assumptions…
We prove a generalization of Gotzmann's persistence theorem in the case of modules with constant Hilbert polynomial. As a consequence, we show that the defining equations that give the embedding of a Quot scheme of points into a…
We prove a general existence theorem for nonlinear partial differential systems of any order in one complex variable. A special case of first order contains a well-known theorem of Nijenhuis and Woolf concerning local existence of…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
The paper develops and studies a very general notion of dichotomy, referred to as "nonuniform $(h,k,\mu,\nu)$-dichotomy". The new notion contains as special cases most versions of dichotomy existing in the literature. The paper then…
As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…
After defining non-Gaussian L\'evy processes for two-sided time, stochastic differential equations with such L\'evy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in…
Recently, Kvalheim and Sontag provided a generalized global Hartman-Grobman theorem for equilibria under asymptotically stable continuous vector fields. By leveraging topological properties of Lyapunov functions, their theorem works without…
In this work, we study nonlocal differential equations with particular focus on those with reflection in their argument and piecewise constant dependence. The approach entails deriving the explicit expression of the solution to the linear…
We prove that if a continuous piecewise-smooth map on $\mathbb{R}^n$ is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important…
In this paper, for iterated function systems, we define the classic concept of the dynamical systems: topological conjugacy of diffeomorphisms. We generalize the Hartman-Grobman theorem for one dimensional iterated function systems on R.…
A linear system of difference equations and a nonlinear perturbation are considered, we obtain sufficient conditions to ensure the topological equivalence between them, namely, the linear part satisfies a property of dichotomy on the…
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…
For homogeneous difference equation of the second order we study the analogy of Hartman-Wintner problem on asymptotic integration of fundamental system of solutions as argument tends to infinity.
This article addresses linear hyperbolic partial differential equations with non-smooth coefficients and distributional data. Solutions are studied in the framework of Colombeau algebras of generalized functions. Its aim is to prove upper…
This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption…
As the title ``Generalized regularity and solution concepts for differential equations'' suggests, the main topic of my thesis is the investigation of generalized solution concepts for differential equations, in particular first order…
In this paper, we first get a criterion formula for whether a differential form is holomorphic with respect to the generalized complex structure induced by $\epsilon$. Next, we get the local extensions of $\overline\partial$-closed forms on…