相关论文: Parameterized Stationary Solution for first order …

G\"{o}del-type metrics that are homogeneous in both space and time remain, like the Schwarzschild metric, consistent within Chern-Simons modified gravity; this is true in both the non-dynamical and dynamical frameworks, each of which…

This work is devoted to the Dirichlet problem for the equation (-\Delta u = \lambda u + |x|^\alpha |u|^{2^*-2} u) in the unit ball of $\mathbb{R}^N$. We assume that $\lambda$ is bigger than the first eigenvalues of the laplacian, and we…

We consider the positive solutions of the nonlinear eigenvalue problem $-\Delta_{\mathbb{H}^n} u = \lambda u + u^p, $ with $p=\frac{n+2}{n-2}$ and $u \in H_0^1(\Omega),$ where $\Omega$ is a geodesic ball of radius $\theta_1$ on…

We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed method is built upon four essential components: (i) a…

This paper deals with existence of solutions to the following fractional $p$-Laplacian system of equations \begin{equation*} %\tag{$\mathcal P$}\label{MAT1} \begin{cases} (-\Delta_p)^s u =|u|^{p^*_s-2}u+…

Kelner, Orecchia, Sidford, and Zhu have given a randomized iterative method for approximating the solution to the discrete Laplace equation that has expected running time nearly linear in the size of the problem. The goal of this note is to…

We describe simple algebraic and combinatorial characterisations of finite relational core structures admitting finitely many obstructions. As a consequence, we show that it is decidable to determine whether a constraint satisfaction…

This paper establishes the conditions of existence of a stationary solution to the first order autoregressive equation on a plane as well as properties of the stationarity solution. The first-order autoregressive model on a plane is defined…

This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…

Motivated by Girsanov's nonuniqueness examples for SDEs, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE) \[\frac{\partial u}{\partial t}=\frac{\Delta}{2}u(t,x)…

Let $\textbf{A}$ be a symmetric convex quadratic form on $\mathbb{R}^{Nn}$ and $\Omega\Subset \mathbb{R}^n$ a bounded convex domain. We consider the problem of existence of solutions $u: \Omega \subset \mathbb{R}^n \longrightarrow…

The main goal of this paper is to prove existence and non-existence results for deterministic Kardar-Parisi-Zhang type equations involving non-local "gradient terms". More precisely, let $\Omega \subset \mathbb{R}^N$, $N \geq 2$, be a…

Let $(u,v)$ be a solution to the Cauchy problem for a semilinear parabolic system \[ \mathrm{(P)} \qquad \cases{ \partial_t u=D_1\Delta u+v^p\quad & $\quad\mbox{in}\quad{\mathbb{R}}^N\times(0,T),$\\ \partial_t v=D_2\Delta v+u^q\quad &…

We study the nonlocal nonlinear problem \begin{equation}\label{ppp} \left\{ \begin{array}[c]{lll} (-\Delta)^s u = \lambda f(u) & \mbox{in }\Omega, \\ u=0&\mbox{on } \mathbb{R}^N\setminus\Omega, \end{array} \right. \tag{$P_{\lambda}$}…

In this paper we consider stationary solutions to the nonlinear one-dimensional Schroedinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark-Wannier ladders of the linear…

We derive explicit expressions for the parameter derivatives $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=0}$ and $[\partial^{3}P_{\nu}(z)/\partial\nu^{3}]_{\nu=0}$, where $P_{\nu}(z)$ is the Legendre function of the first kind. It is…

In this paper, we study the existence of nodal solutions for the non-autonomous Schr\"{o}dinger--Poisson system: \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+u+\lambda K(x) \phi u=f(x) |u|^{p-2}u & \text{ in }\mathbb{R}^{3}, \\…

Integration operational matrix methods based on Zernike polynomials are used to determine approximate solutions of a class of non-homogeneous partial differential equations (PDEs) of first and second order. Due to the nature of the Zernike…

In this paper, we study the existence of ground state solutions for the nonlinear fractional Schr\"{o}dinger-Poisson system \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^su+V(x)u+\phi u=|u|^{p-1}u, & \hbox{in $\mathbb{R}^3$,}…

The purpose of the present work is to study the existence of solutions to initial value problems for nonlinear first order differential systems with nonlinear nonlocal boundary conditions of functional type. The existence results are…