Related papers: Existence of $\partial$-parameterized Picard-Vessi…
We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on differential calculus in a simple canonical form…
This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear…
We establish a microscopic convexity principle for nonlinear elliptic and parabolic partial differential equations in general form.
We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…
In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.
This short note aims to give an insight to Arveson's boundary theorem by means of non-commutative Poisson boundaries and its applications.
This note is devotes to some remarks regarding the use of variational methods, of minimax type, to establish continuity type results
In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum.
In this short note we prove a lemma about the dimension of certain algebraic sets of matrices. This result is needed in our paper arXiv:1201.1672. The result presented here has also applications in other situations and so it should appear…
We give an extensive list of parametrized families of polynomial continued fractions of smallest possible degrees for $\pi^2$ and $\zeta(3)$, and mention similar results for other constants.
We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prove that the approach is arbitrarily high-order and also show…
The $P_1$--nonconforming quadrilateral finite element space with periodic boundary condition is investigated. The dimension and basis for the space are characterized with the concept of minimally essential discrete boundary conditions. We…
There is a serious discrepancy among literature on the Picard-Vessiot theory in positive characteristics (for iterative differential fields). It is about descriptions of Galois correspondence. We should use affine group schemes instead of…
We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…
Let $F$ be a $\delta-$field (differential field) of characteristic zero with an algebraically closed field of constants $F^\delta$, $A$ be a $\delta-F-$central simple algebra, $K$ be a Picard-Vessiot extension for the $\delta-F-$module $A$…
This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.
The purpose of this short note is to show how it is possible to combine existing results in the literature to get the unique continuation from sets of positive measure for time dependent parabolic equations with Lipschitz principal part and…
The purpose of this technical note is to summarize the relationship between the marginal variance and correlation length of a Gaussian random field with Mat\'ern covariance and the coefficients of the corresponding…
We propose a framework to define solutions of ODE systems under a novel condition that goes well beyond the usual continuity condition required in the classical theory of ODEs (Peano's or Picard's theorems). We illustrate our results with…
Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of…