Existence and Uniqueness for Nonlinear Integro-Differential Equations in Real Locally Complete Spaces

Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space

The main purpose is to generalize a theorem of Arendt about uniqueness of $C_0$-semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for $C_0$-semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport equation has one unique $L^1(\R^d,dx)$ weak solution.

带时滞的积分微分方程：一种扰动方法

Integro-differential equations with delays: A perturbation approach

本文针对带时滞的积分微分方程提出扰动方法，建立经典解与温和解的存在唯一性及常数变易公式，并修正了先前文献中一个基本定理的陈述与证明。

A note on the uniqueness of involution in locally C*-algebras

In the present note we show that the involution in locally C*-algebras is uniquely determined.

Existence and Uniqueness of Solutions to Nonlinear Evolution Equations with Locally Monotone Operators

In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators. In particular, we show that local monotonicity implies the pseudo-monotonicity. The main result is applied to various types of PDE such as reaction-diffusion equations, generalized Burgers equation, Navier-Stokes equation, 3D Leray-$α$ model and $p$-Laplace equation with non-monotone perturbations.

Approximation Properties of Locally Convex Spaces and the Problem of Uniqueness of the Trace of a Linear Operator

In the present article, it is proved that every nuclear operator in a locally convex space E has a well-defined trace if E possesses the approximation property. However, even if a space possesses the approximation property this still does not guarantee a positive solution of A. Grothendieck's uniqueness problem for this space. Below, we present an example of a quasi-complete space with the approximation property in which it is not possible to define the trace for all Fredholm operators (in the sense of A. Grothendieck). We prove that the uniqueness problem has a positive solution if E possesse…

局部凸空间中Hahn-Banach延拓的唯一性

Uniqueness of Hahn-Banach extensions in locally convex spaces

本文研究局部凸空间中线性泛函的Hahn-Banach延拓唯一性，提出property-SNP并给出其多种刻画，建立其与Banach空间property-U的对应关系，还在逐点收敛拓扑下的连续函数空间上开展相关研究。

抛物型方程与系统的基本解：普适存在性、唯一性与表示

Fundamental solutions for parabolic equations and systems: universal existence, uniqueness, representation

本文提出一种普适变分方法，在最小假设下证明抛物型方程弱解柯西问题的适定性，建立基本解的存在唯一性及其与演化族的一致性，并通过三个具体应用验证结果。

分次李群上的积分-微分扩散方程

Integro-differential diffusion equations on graded Lie groups

该研究针对分次李群上的一类含时间非局部算子与正Rockland算子的积分-微分扩散方程，利用群傅里叶分析得到显式解，证明其适定性，给出范数估计、时间衰减率及紧李群对应结果。

关于预对偶的线性化与唯一性

On linearisation and uniqueness of preduals

本文研究局部凸豪斯多夫函数空间的强线性化与预对偶唯一性，给出将强线性化从标量值提升到向量值情形的充分条件，并据此刻画具有（强）唯一预对偶的bornological空间。

The abstract Cauchy problem in locally convex spaces

We derive sufficient criteria for the uniqueness and existence of solutions of the abstract Cauchy problem in locally convex Hausdorff spaces. Our approach is based on a suitable notion of an asymptotic Laplace transform and extends results of Langenbruch beyond the class of Fréchet spaces.

局部凸空间中的抽象非自治差分包含

Abstract nonautonomous difference inclusions in locally convex spaces

本文研究局部凸空间中抽象非自治差分包含的概周期型解的存在性与唯一性，所得结果在Banach空间情形下也是全新的。

$C^*$-uniqueness Results for Groupoids

For a second-countable locally compact Hausdorff étale groupoid $\mathcal{G}$ with a continuous $2$-cocycle $σ$ we find conditions that guarantee that $\ell^1 (\mathcal{G},σ)$ has a unique $C^*$-norm.

Nonlocal complement value problem for a global in time parabolic equation

The overreaching goal of this paper is to investigate the existence and uniqueness of weak solution of a semilinear parabolic equation with double nonlocality in space and in time variables that naturally arises while modeling a biological nano-sensor in the chaotic dynamics of a polymer chain. In fact, the problem under consideration involves a symmetric integrodifferential operator of Lévy type and a term called the interaction potential, that depends on the time-integral of the solution over the entire interval of solving the problem. Owing to the Galerkin approximation, the existence and u…

Linear Monotone Subspaces of Locally Convex Spaces

The main focus of this paper is to study multi-valued linear monotone operators in the contexts of locally convex spaces via the use of their Fitzpatrick and Penot functions. Notions such as maximal monotonicity, uniqueness, negative-infimum, and (dual-) representability are studied and criteria are provided.

具有局部Lipschitz系数和粗糙初始数据的多维半线性随机偏微分方程的存在性、唯一性和路径正则性

Existence, Uniqueness, and Pathwise Regularity for Multidimensional Semilinear SPDEs with Locally Lipschitz Coefficients and Rough Initial Data

研究由乘性噪声驱动、具粗糙初始数据的多维半线性随机演化方程，在系数全局Lipschitz时建解的适定性等，局部Lipschitz时证最大局部解相关性质，条件针对特定范数，可用于多种方程及处理奇异和非光滑初始数据。