Non-abelian Vortices: Existence, Uniqueness and Asymptotics

We provide a unified approach in the (analytical) study of non-abelian vortices for the models proposed in [4, 7]. We also obtain the necessary estimates to describe the asymptotic behavior of a vortex configuration under a regime of physical interest.     

Large Solutions to Complex Monge-Amp`ere Equations:Existence, Uniqueness and Asymptotics

The authors consider the complex Monge-Ampère equation det( u_i[`(j)] )\left( {u_{i\bar j} } \right) = ψ(z, u, ∇ u) in bounded strictly pseudoconvex domains Ω, subject to the singular boundary condition u = ∞ on ∂Ω. Under suitable conditions on ψ, the existence, uniqueness and the exact asymptotic behavior of solutions to boundary blow-up problems for the complex Monge-Ampère equations are established.     

Existence and Uniqueness of F-Minimal Surfaces

We extend a classical result of Radó and Kneser concerning uniqueness ofminimal surfaces bounded by a given closed Jordan curve in³ to the case of extremals for certain geometric variationalintegrals. Using standard elliptic PDE theory, this gives the existenceand uniqueness of embedded F-minimal surfaces for suitable boundarycurves that project simply onto the boundary of a plane convex domain.     

一般非线性渗流方程广义解的存在唯一性与Blow-up

In this paper,we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations ut-Dj(aij(x,t,u)Diφ(u))+bi(t,u)Diu+C(x,t,u)=0,and obtain the existence,uniqueness and blow-up in finite time of these solutions under some structure conditions.     

������������������Ⱥ���̽�Ĵ���Ψһ��

??In this paper, we introduce a class of stochastic age-dependent population equations with Poisson jumps. Existence and uniqueness of energy solutions for stochastic age-dependent population dynamic system are proved under local non-Lipschitz condition in Hilbert space.     

Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems

For a given finite subset S of a compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M\S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the conformal metric belongs to the boundary of the given cone. As a by-product, we define a purely local notion of Ricci lower bounds for continuous metrics that are conformal to smooth metrics and prove a corresponding volume comparison theorem. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.     

Existence and Uniqueness of Solutions to Random Impulsive Differential Systems

The existence and uniqueness in mean square of solutions to certain random impulsive differentialsystems is discussed in this paper.Cauchy-Schwarz inequality,Lipschtiz condition and techniques in stochasticanalysis are employed in achieve the desired results.     

S—R分解定理的唯一性,存在性和客观性

对于连续体的一切物理可能的变形场，其变形梯度张量F可被分解为一个对称张量S和一个正交张量R的直和，这便是S-R分解定理．本文通过矩阵方法和张量方法证明了S-R分解定理的唯一性、存在性和客观性．     

Spectral Bounds for Tricomi Problems and Application to Semilinear Existence and Existence with Uniqueness Results

For the linear Tricomi problem, it is shown that real eigenvalues corresponding to generalized eigenfunctions must be positive and that the energy integral methods used to prove solvability results can give lower bounds on the spectrum. Exploiting the linear solvability theory and spectral information, standard nonlinear analysis tools are employed to yield results on existence and uniqueness for semilinear problems. In particular, using the Leray-Schauder principle, existence of generalized solutions with sublinear nonlinearities is established. For sublinear or asymptotically linear nonlinearities that satisfy a Lipschitz condition, the contraction mapping principle is employed to give results on existence with uniqueness. The Lipschitz constant depends on lower bounds for the spectrum of the linear problem. For certain superlinear problems, maximum principles for the linear problem are used via the method of upper and lower solutions to give results on existence.     

Global Existence, Uniqueness and Pathwise Property of Solutions to a Stochastic R¨ossler-Lorentz System

The authors integrate two well-known systems, the R¨ossler and Lorentz systems, to introduce a new chaotic system, called the Lorentz-R¨ossler system. Then, taking into account the effect of environmental noise, the authors incorporate white noise in both R¨ossler and Lorentz systems to have a corresponding stochastic system. By deriving the uniform a priori estimates for an approximate system and then taking them to the limit, the authors prove the global existence, uniqueness and the pathwise property of solutions to the Lorentz-R¨ossler system. Moreover, the authors carried out a number of numerical experiments, and the numerical results demonstrate their theoretic analysis and show some new qualitative properties of solutions which reveal that the Lorentz-R¨ossler system could be used to design more complex and more secure nonlinear hop-frequence time series.     

Existence and Uniqueness of Weak Solutions to the $p$-Biharmonic Parabolic Equation

We consider an initial-boundary value problem for a $p$-biharmonic parabolic equation. Under some assumptions on the initial value, we construct approximate solutions by the discrete-time method. By means of uniform estimates on solutions of the time-difference equations, we establish the existence of weak solutions, and also discuss the uniqueness.     

时滞Duffing型方程周期解的存在唯一性

该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t)$ 该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t)$ 该文利用拓扑度方法研究了一类时滞依赖状态的广义Duffing型泛函微分方程x'(t) g(x(t-τ(t,x(t))))=f(t)周期解的存在性,得到了方程周期解存在的充分条件和必要条件．研究了当滞量为常值时,方程周期解的存在唯一性．并且给出了所研究问题的一个应用实例．     

分数Brown运动驱动的随机延迟微分方程解的存在唯一性

研究了Hirst参数H>1/2分数Brown运动驱动的随机延迟微分方程(SDDE),随机积分如Duncan et al.[9]所定义的Wick-It■型随机积分,在系数具有充分正则性条件下,证明了随机延迟微分方程解的存在唯—性,其中利用了Malliavinφ-导数及随机分析。     

分数Brown运动驱动的随机延迟微分方程解的存在唯一性

研究了Hirst参数H＞1/2分数Brown运动驱动的随机延迟微分方程(SDDE).随机积分如Duncan et al.[9]所定义的Wick-It(o)型随机积分,在系数具有充分正则性条件下,证明了随机延迟微分方程解的存在唯一性,其中利用了Malliavin φ-导数及随机分析.     

Existence and Uniqueness of Martingale Solutions to Option Pricing Equations with Noise

Lithuanian Mathematical Journal - We introduce a new option pricing equation with noise in a frictional financial market, which is fully different from the classical option pricing equation, and...     

Existence and Uniqueness to a Dynamic Bilateral Frictional Contact Problem in Viscoelasticity

In this paper we examine an evolution problem which describes the dynamic bilateral contact of a viscoelastic body and a foundation. The contact is modeled by a friction multivalued subdifferential boundary condition which incorporates the Coulomb law of friction, the SJK model and the orthotropic friction law. The main result concerns the existence and uniqueness of weak solutions to the hyperbolic variational inequality when the friction coefficient is sufficiently small. The proof is based on a surjectivity result for multivalued operators and a fixed point argument. Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.     

Koiter壳动力学方程解的存在性和唯一性

用Galerkin方法研究了Koiter壳动力学方程,得到了解的存在性与唯一性结果。