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We extend Kolchin's results on linear dependence over projective varieties in the constants, to linear dependence over arbitrary complete differential varieties. We show that in this more general setting, the notion of linear dependence…

In this paper, we consider a generalized strong vector quasi-equilibrium problem and we prove the existence of its solutions by using some suxiliary results. One of the established theorems is proved by using an approximation method.

There is studied problem on solvability of linear non-homogeneous differential equation of higher even order. There is proved the theorem on necessary and sufficient conditions on existence of solutions to the equation in the Schwartz…

The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.

We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…

A priori estimates for finite-difference approximations for the first and second order derivatives are obtained for solutions of parabolic equations described in the title.

For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…

In this note, we establish a new Carleman estimate with singular weights for the sub-Laplacian on a Carnot group $\mathbb G$ for functions satisfying the discrepancy assumption in (2.16) below. We use such an estimate to derive a sharp…

In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.

In this paper, we prove that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N distinguishable particles, to within 1/ ln(N ). This intruiguing result is related to recent developments in…

We discuss the Carleman linearization approach to the quantum simulation of classical fluids based on Grad's generalized hydrodynamics and compare it to previous investigations based on lattice Boltzmann and Navier-Stokes formulations. We…

We describe a Quillen equivalence between quasi-categories and relative categories which is surprisingly similar to Thomason's Quillen equivalences between simplicial sets and categories.

In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that we employ a particular embedding (Carleman linearization) to…

We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.

In this paper, we study the existence and non-existence of entire solutions of certain non-linear delay-differential equations.

We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…

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…

We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hoelder's Theorem that the Gamma function satisfies no…

By virtue of numerical arguments we study a bifurcation phenomenon occurring for a class of minimization problems associated with the quasi-linear Schrodinger equation.

We study a class of linearly coupled system of quasilinear equations. Under some assumptions on the nonlinear terms, we establish some results about the existence and regularity of vector solutions for the p-Laplacian systems by using…