Related papers: Remarks on the Ostrovsky's Theorem

In this paper we study the problems of the following kind: For a pair of topological spaces $X$ and $Y$ find sufficient conditions that under every continuous map $f : X\to Y$ a pair of sufficiently distant points is mapped to a single…

We construct whole-space extensions of functions in a fractional Sobolev space of order $s\in (0,1)$ and integrability $p\in (0,\infty)$ on an open set $O$ which vanish in a suitable sense on a portion $D$ of the boundary $\partial O$ of…

We study the periodic Ostrovsky-Hunter equation in the case where the flux function may depend on the spatial variable. Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution.…

The global boundness, existence and uniqueness are presented for the kind of Rosseland equation with a small parameter. This problem comes from conduction-radiation coupled heat transfer in the composites; it's with coefficients of high…

In a recent paper we proved that if (*)=\inf_{|z_k|=1}\max_{v=1,...,n^2-n} |\sum_{k=1}^n z_k^v|, then (*)=\sqrt{n-1} if n-1 is a prime power. We proved that a construction of Fabrykowski gives minimal systems (z_1,...,z_n) to this problem.…

We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function $f\in L^p$ with $p>1$, i.e. bi-Sobolev solutions for the prescribed Jacobian inequality in the plane for right-hand sides $f\in…

We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…

We provide an affirmative answer to the Cr Closing Lemma, r>1, for a large class of flows defined on every closed surface.

We show that multiplication from $L_p\times L_q$ to $L_1$ (for $p,q\in [1,\infty]$, $1/p+1/q=1$) is a uniformly open mapping. We also prove the uniform openness of the multiplication from $\ell_1\times c_0$ to $\ell_1$. This strengthens the…

The classical Sturm-Hurwitz-Kellogg theorem asserts that a function, orthogonal to an n-dimensional Chebyshev system on a circle, has at least n+1 sign changes. We prove the converse: given an n-dimensional Chebyshev system on a circle and…

Let $\Omega=(a,b)\subset\mathbb{R}$, $0\leq m,n\in L^{1}(\Omega)$, $\lambda,\mu>0$ be real parameters, and $\phi:\mathbb{R}\rightarrow\mathbb{R}$ be an odd increasing homeomorphism. In this paper we consider the existence of positive…

We use a novel transformation of the reduced Ostrovsky equation to the integrable Tzitz\'eica equation and prove global existence of small-norm solutions in Sobolev space $H^3(R)$. This scenario is an alternative to finite-time wave…

In this paper we show that the piecewise linear map f(x) = px for x in [0,1/p], and sx-s/p for x in (1/p,1], p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding and exact.

The L'vov-Kaplansky conjecture states that the image of a multilinear noncommutative polynomial $f$ in the matrix algebra $M_n(K)$ is a vector space for every $n \in {\mathbb N}$. We prove this conjecture for the case where $f$ has degree…

Let $p$ be a polynomial in several non-commuting variables with coefficients in a field $K$ of arbitrary characteristic. It has been conjectured that for any $n$, for $p$ multilinear, the image of $p$ evaluated on the set $M_n(K)$ of $n$ by…

We characterize the polynomials $p_1(t), ... , p_n(t)$ whose Wronskian $W(p_1, ... , p_n)$ is a nonzero constant. Then, we generalize our results to characterize the Laurent polynomials with the same property. Finally, for rational…

We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a mapping also respects matrix similarities, i.e., is a…

We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second…

In this paper, we prove that every continuous $h$-mid-convex with suitable conditions on $h$ is $h$-convex function. Also, we extend Ostrowski theorem, Blumberg-Sierpinski theorem, Bernstein-Doetsch theorem, Mehdi theorem.

In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to…