A note on existence and uniqueness of limit cycles for Liénard systems

A note on discrete Heisenberg uniqueness pairs for the parabola

We discuss on Heisenberg uniqueness pairs for the parabola given by discrete sequences along straight lines. Our method consists in linking the problem at hand with recent uniqueness results for the Fourier transform.

A note on Riemann-Liouville fractional Sobolev spaces

Taking inspiration from a recent paper by Bergounioux, Leaci, Nardi and Tomarelli we study the Riemann-Liouville fractional Sobolev space $W^{s, p}_{RL, a+}(I)$, for $I = (a, b)$ for some $a, b \in \mathbb{R}, a < b$, $s \in (0, 1)$ and $p \in [1, \infty]$; that is, the space of functions $u \in L^{p}(I)$ such that the left Riemann-Liouville $(1 - s)$-fractional integral $I_{a+}^{1 - s}[u]$ belongs to $W^{1, p}(I)$. We prove that the space of functions of bounded variation and the fractional Sobolev space, $BV(I)$ and $W^{s, 1}(I)$, continuously embed into $W^{s, 1}_{RL, a+}(I)$. In addition, …

A note on uniqueness of extension for characteristic functions

Let $f:R\to C$ be the characteristic function of a probability measure. We study the following question: Is it true that for any closed interval $I$ on $R$, which does not contain the origin, there exists a characteristic function $g$ such that $g$ coincides with $f$ on $I$ but $g \not\equiv f$ on $R$?

Uniqueness of exterior differentiation on locally finite graphs

In this short note, we prove the uniqueness of exterior differentiation on locally finite graphs.

A note on the well posed anisotropic discrete BVP's

Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions.

初值问题解的存在性与唯一性的一个初等证明

An elementary proof of the existence and uniqueness of solutions to an initial value problem

本文用纯初等分析工具（不涉及积分）证明了Lipschitz条件下初值问题解的局部存在性与唯一性，通过Cauchy迭代在稠密子集收敛并延拓至全区间。