相关论文: On a class of semilinear fractional elliptic equat…

In this paper, we classify the singularities of nonnegative solutions to fractional elliptic equation \begin{equation}\label{eq 0.1} \arraycolsep=1pt \begin{array}{lll} \displaystyle (-\Delta)^\alpha u=u^p\quad &{\rm in}\quad…

Let $p\in(0,\frac{N}{N-2\alpha})$, $\alpha\in(0,1)$ and $\Omega\subset \R^N$ be a bounded $C^2$ domain containing $0$. If $\delta_0$ is the Dirac measure at $0$ and $k>0$, we prove that the weakly singular solution $u_k$ of $(E_k)$ $…

The purpose of this paper is to study the weak solutions of the fractional elliptic problem \begin{equation}\label{000} \begin{array}{lll} (-\Delta)^\alpha u+\epsilon g(u)=k\frac{\partial^\alpha\nu}{\partial \vec{n}^\alpha}\quad &{\rm…

In this paper, we study the following elliptic problem with Dirac mass \begin{equation}\label{eq 0.1} -\Delta u=Vu^p+k \delta_0\quad {\rm in}\quad \mathbb{R}^N, \qquad \lim_{|x|\to+\infty}u(x)=0, \end{equation} where $N>2$, $p>0$, $k>0$,…

We study the existence of solutions to the fractional elliptic equation (E1) $(-\Delta)^\alpha u+\epsilon g(|\nabla u|)=\nu $ in a bounded regular domain $\Omega$ of $\R^N (N\ge2)$, subject to the condition (E2) $u=0$ in $\Omega^c$, where…

The purpose of this article is to study very weak solutions of elliptic equation $$ -\Delta u+g(u)=2k\frac{\partial \delta_0}{\partial x_N }+j\delta_0\quad {\rm in}\quad\ \ B_1(0),\qquad u=0\quad {\rm on}\quad\ \ \partial B_1(0), $$ where…

In this paper we consider the existence and multiplicity of weak solutions for the following class of fractional elliptic problem \begin{equation}\label{00} \left\{\begin{aligned} (-\Delta)^{\frac{1}{2}}u + u &= Q(x)f(u)\;\;\mbox{in}\;\;\R…

In this paper, we study the existence of nonnegative weak solutions to (E) $ (-\Delta)^\alpha u+h(u)=\nu $ in a general regular domain $\Omega$, which vanish in $\R^N\setminus\Omega$, where $(-\Delta)^\alpha$ denotes the fractional…

In the present paper we investigate the following semilinear singular elliptic problem: \begin{equation*} (\rm P)\qquad \left \{\begin{array}{l} -\Delta u = \dfrac{p(x)}{u^{\alpha}}\quad \text{in} \Omega \\ u = 0\ \text{on} \Omega,\ u>0…

This paper is devoted to the study of the existence of positive solutions for a problem related to a higher order fractional differential equation involving a nonlinear term depending on a fractional differential operator,…

We study the existence of weak solutions of (E) $ (-\Delta)^\alpha u+g(u)=\nu $ in a bounded regular domain $\Omega$ in $\R^N (N\ge2)$ which vanish on $\R^N\setminus\Omega$, where $(-\Delta)^\alpha$ denotes the fractional Laplacian with…

In this paper, we consider the regularity of weak solutions (in an appropriate space) to the elliptic partial differential equation \begin{equation*} (-\Delta_{p})^{s} u + (-\Delta_{q})^{s} u = f(x) \quad \text{in} \quad \mathbb{R}^{N},…

The aim of this paper is to study the singular solutions to fractional elliptic equations with absorption $$ \left\{\arraycolsep=1pt \begin{array}{lll} (-\Delta)^\alpha u+|u|^{p-1}u=0,\quad & \rm{in}\quad\Omega\setminus\{0\},\\[2mm]…

In this work, we study the existence of weak solution to the following quasi linear elliptic problem involving the fractional $p$-Laplacian operator, a Hardy potential and multiple critical Sobolev nonlinearities with singularities,…

In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to the nonlinear fractional elliptic problem of type $(P)$ (see below) involving singular nonlinearity and singular weights in smooth…

In this paper we study some nonlinear elliptic equations in $\R^n$ obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is $$ (-\Delta)^s u = \epsilon\,h\,u^q + u^p \ {{in}}\R^n,$$ where $s\in(0,1)$,…

In this paper we study existence, regularity, and approximation of solution to a fractional semilinear elliptic equation of order $s \in (0,1)$. We identify minimal conditions on the nonlinear term and the source which leads to existence of…

In this article, we prove the existence of solutions to a nonlinear nonlocal elliptic problem with a singualrity and a discontinuous critical nonlinearity which is given as follows. \begin{align} \begin{split}\label{main_prob}…

This article concerns the fractional elliptic equations \begin{equation*}(-\Delta)^{s}u+\lambda V(x)u=f(u), \quad u\in H^{s}(\mathbb{R}^N), \end{equation*}where $(-\Delta)^{s}$ ($s\in (0\,,\,1)$) denotes the fractional Laplacian, $\lambda…

The purpose of this paper is to study nonlinear singular parabolic equations with $p(x)$- Laplacian. Precisely, we consider the following problem and discuss the existence of a non-negative weak solution. \begin{align*} \frac{\partial…