Related papers: Some remarks on Davie's uniqueness theorem
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…
The purpose of this paper is to study the existence and uniqueness of solutions to a system of Stochastic Differential Equations (SDEs). The coordinates are bounded by zero and one, and repulse each other according to a Coulombian like…
A class of backward doubly stochastic differential equations (BDSDEs in short) with continuous coefficients is studied. We give the comparison theorems, the existence of the maximal solution and the structure of solutions for BDSDEs with…
Consider the equation $$ u'(t)-\Delta u+|u|^\rho u=0, \quad u(0)=u_0(x), (1), $$ where $ u':=\frac {du}{dt}$, $ \rho=const >0, $ $x\in \mathbb{R}^3$, $t>0$. Assume that $u_0$ is a smooth and decaying function, $$\|u_0\|\:=\sup_{x\in…
We summarize results concerning the Bernstein property of differential equations.
In this paper, we study a class of multi-dimensional reflected backward stochastic differential equations when the noise is driven by a Brownian motion and an independent Poisson point process, and when the solution is forced to stay in a…
Let $B=\{ B_{t}\} _{t\ge 0}$ be a one-dimensional standard Brownian motion. As an application of a recent result of ours on exponential functionals of Brownian motion, we show in this paper that, for every fixed $t>0$, the process given by…
In this paper, we obtain the existence and uniqueness theorem for backward stochastic differential equation driven by G-Brownian motion (G-BSDE) under degenerate case. Moreover, we propose a new probabilistic method based on the…
This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several…
In this paper, we investigate the stochastic differential equation on $\mathbb{R}^d,d\geq2$: \begin{align*} \dif X_t&=v(t,X_t)\dif t+\sqrt{2} \dif W_t. \end{align*} For any finite collection of initial probability measures…
We prove the uniqueness theorem for the solutions to the restricted Weyl commutation relations braiding unitary groups and semi-groups of contractions that are close to unitaries. We also discuss related mathematical problems of continuous…
We develop a general theory of intertwined diffusion processes of any dimension. Our main result gives an SDE construction of intertwinings of diffusion processes and shows that they correspond to nonnegative solutions of hyperbolic partial…
In this paper we prove that the lack of uniqueness for solutions of the tree dyadic model of turbulence is overcome with the introduction of a suitable noise. The uniqueness is a weak probabilistic uniqueness for all $l^2$-initial…
We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized…
In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…
In this paper, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations (anticipated BDSDEs). The coefficients of these BDSDEs depend on the future value of the solution $(Y,…
We define compositions $\varphi(X)$ of H\"older paths $X$ in $\mathbb{R}^n$ and functions of bounded variation $\varphi$ under a relative condition involving the path and the gradient measure of $\varphi$. We show the existence and…
We construct a family of velocity fields demonstrating the sharpness of the classical Zvonkin--Veretennikov--Davie strong well-posedness by noise regime. We consider stochastic differential equations driven by Brownian noise with drift $u$…
We investigate the existence and multiplicity of solutions for higher order discrete boundary value problems via critical point theory.
We investigate the existence and multiplicity of solutions for fourth order discrete boundary value problems via critical point theory.