Related papers: Relaxed commutant lifting: existence of a unique s…
The pure traction problem of elasticity appears frequently in engineering applications, and its complexity stems from the fact that its solution is unique only up to (infinitesimal) rigid body motions. When finite elements are employed to…
In this note, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal . As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.
We study a single column model of moist convection in the atmosphere. We state the conditions for it to represent a stable steady state. We then evolve the column by subjecting it to an upward displacement which can release instability,…
We consider sufficient conditions which guarantee that a planar embedding has a unique fixed point. We study sufficient conditions which imply the appearing of a globally attracting fixed point for such an embedding.
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…
The object of the present paper is to find new sufficient conditions for the existence of unique strong solutions to a class of (time-inhomogeneous) stochastic differential equations with random, non-Lipschitzian coefficients. We give an…
In terms of initial data, a sufficient condition for the smoothness of the solution to the Cauchy problem for one-dimensional relativistic cold plasma equations over any given time interval is found. Unlike the non-relativistic case, such…
First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…
A set of coupled conditions consisting of differential-difference equations is presented for Casorati determinants to solve the Toda lattice equation. One class of the resulting conditions leads to an approach for constructing complexiton…
In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
In this paper, we investigate new sufficient conditions to ensure the existence of a unique global strong solution of stochastic differential equations with jumps. By using Euler approximation and by utilising a new test function…
We give necessary and sufficient conditions for a pair of (generalized) functions $\rho_1(\mathbf{r}_1)$ and $\rho_2(\mathbf{r}_1,\mathbf{r}_2)$, $\mathbf{r}_i\in X$, to be the density and pair correlations of some point process in a…
In this paper we give a general condition on the absorption term of the 1-Laplace elliptic equation for the existence of suitable large solutions. This condition can be considered as the correspondent Keller-Osserman condition for the…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
We establish the uniqueness of solutions of the Camassa-Holm equation on a finite interval with non-homogeneous boundary conditions in the case of bounded momentum. A similar result for the higher-order Camassa-Holm system is also given.…
Consider a nonzero contraction $T$ and a bounded operator $X$ satisfying $TX=qXT$ for a complex number $q$. There are some interesting results in the literature on $q$-commuting dilation and $q$-commutant lifting of such pair $(T,X)$ when…
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the…
The classical Melan equation modeling suspension bridges is considered. We first study the explicit expression and the uniform positivity of the analytical solution for the simplified ``less stiff'' model, based on which we develop a…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…