Related papers: Fractional Hardy-Sobolev equations with nonhomogen…
In this work we analyze a class of nonlinear fractional elliptic systems involving Hardy--type potentials and coupled by critical Hardy-Sobolev--type nonlinearities in $\mathbb{R}^N$. Due to the lack of compactness at the critical exponent…
In this article, we derive the existence of positive solutions of a semi-linear, non-local elliptic PDE, involving a singular perturbation of the fractional laplacian, coming from the fractional Hardy-Sobolev-Maz'ya inequality, derived in…
We investigate the existence of positive solutions to fractional equations presenting a double criticality: a multi-polar Hardy-type potential and a Sobolev critical nonlinearity. The nonlocal nature of the operator and the absence of…
By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical…
This paper is devoted to study a fractional Choquard problem with slightly subcritical exponents on bounded domains. When the exponent of the convolution type nonlinearity tends to the fractional critical one in the sense of…
The aim of this paper is to study a class of nonlocal fractional Laplacian equations depending on two real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci, we…
We are concerned with a Brezis-Nirenberg type problem for a critical Choquard equation, in the sense of Hardy-Littlewood-Sobolev inequality, and with the Hardy potential in a smooth bounded domain. By exploiting variational methods we…
In this paper, we consider a fractional p-Laplacian system of equations in the entire space RN with doubly critical singular nonlinearities involving a local critical Sobolev term together with a nonlocal Choquard critical term; the problem…
This paper deals with existence and multiplicity of positive solutions to the following class of nonlocal equations with critical nonlinearity: \begin{equation} \tag{$\mathcal E$} (-\Delta)^s u = a(x)…
In this paper we study positive solutions to the following nonlocal system of equations: \begin{equation*} \left\{\begin{aligned} &(-\Delta)^s u = \frac{\alpha}{2_s^*}|u|^{\alpha-2}u|v|^{\beta}+f(x)\;\;\text{in}\;\mathbb{R}^{N},…
In this paper, we study the existence and qualitative properties of positive solutions to a Choquard-type equation with Hardy potential. We develop a nonlocal version of concentration-compactness principle involving the Hardy potential to…
In this paper, we study the following fractional nonlocal Sobolev-type inequality \begin{equation*} C_{HLS}\bigg(\int_{\mathbb{R}^n}\big(|x|^{-\mu} \ast |u|^{p_s}\big)|u|^{p_s}…
We apply a topological method to prove existence of positive solutions for the nonlineair Choquard equation with upper critical exponent in the sense of Hardy-Littlewood-Sobolev inquality on bounded domains having nontrivial homology group.
In this article, we study the following nonlinear doubly nonlocal problem involving the fractional Laplacian in the sense of Hardy-Littlewood-Sobolev inequality \begin{equation*} \left\{\begin{aligned} (-\Delta)^s u & =…
This paper deals with existence of a nontrivial positive solution to systems of equations involving nontrivial nonhomogeneous terms and critical or subcritical nonlinearities. Via a minimization argument we prove existence of a positive…
In this paper, we consider the nonlocal elliptic problems in $\mathbb{R}^{N}$, which involve finite many critical exponents. By using endpoint refined Hardy--Sobolev inequality, fractional Coulomb--Sobolev space and variational method, we…
In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave-convex nonlinearities: $$({-}{ \Delta})^{\frac{\alpha}{2}}u- \gamma \frac{u}{|x|^{\alpha}}=…
The main objective of this paper is to study the existence of solutions to some basic fractional difference equations. The tools employed are Krasnosel'skii fixed point theorem which guarantee at least two positive solutions.
We study the existence/nonexistence and qualitative properties of the positive solutions to the problem \begin{align*} (-\Delta)^s u -\theta\frac{u}{|x|^{2s}}&=u^p - u^q \quad\text{in }\,\, \mathbb{R}^N,\quad u > 0 \quad\text{in }\,\,…
We exhibit existence of non-trivial solutions of some fractional linear Schr\"odinger equations which are radial and vanish at the origin. This is in stark contrast to what happens in the local case. We also prove analogous results in the…