Related papers: Fractional Hardy-Sobolev equations with nonhomogen…
By exploiting a suitable Trudinger-Moser inequality for fractional Sobolev spaces, we obtain existence and multiplicity of solutions for a class of one-dimensional nonlocal equations with fractional diffusion and nonlinearity at exponential…
We study existence and multiplicity of positive solutions of the following class of nonlocal scalar field equations: \begin{equation} \tag{$\mathcal{P}$} \left\{\begin{aligned} (-\Delta)^s u + u &= a(x)…
In this paper we study existence and nonexistence of nonnegative distributional solutions for a class of semilinear fractional elliptic equations involving the Hardy potential.
The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result…
In this paper we consider the fractional nonlinear Schr\"odinger equation $$\varepsilon^{2s}(-\Delta)^s v+ V(x) v= f(v), \quad x \in \mathbb{R}^N$$ where $s \in (0,1)$, $N \geq 2$, $V \in C(\mathbb{R}^N,\mathbb{R})$ is a positive potential…
We study linear and non-linear equations related to the fractional Hardy--Sobolev inequality. We prove nondegeneracy of ground state solutions to the basic equation and investigate existence and qualitative properties, including symmetry of…
We study a fractional $p$-Laplace equation involving a variable exponent singular nonlinearity in the framework of the Heisenberg group. We first establish the existence and regularity of weak solutions. In the case of a constant singular…
This paper deals with the following nonlocal system of equations: \begin{align}\tag{$\mathcal S$}\label{MAT1} (-\Delta_p)^s u = \frac{\alpha}{p_s^*}|u|^{\alpha-2}u|v|^{\beta}+f(x) \text{ in } \mathbb{R}^{d}, \, (-\Delta_p)^s v =…
Although quantitative stability for critical points of the Sobolev and fractional Sobolev inequalities has been extensively studied, the corresponding stability theory for critical points of the Hardy--Littlewood--Sobolev (HLS) inequality…
The present work is concerned with existence of positive solutions for a class of fractional equation involving a Kirchhoff term and singular potential.
This paper is concerned with the following fractional Schr\"odinger equation \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^{s} u+u= k(x)f(u)+h(x) \mbox{ in } \mathbb{R}^{N}\\ u\in H^{s}(\R^{N}), \, u>0 \mbox{ in } \mathbb{R}^{N},…
In this paper, we establish some Harnack type inequalities satisfied by positive solutions of nonlocal inhomogeneous equations arising in the description of various phenomena ranging from population dynamics to micro-magnetism. For regular…
This paper concerns positive solutions to the boundary value problems of the scalar field equation in the half space with a Sobolev supercritical nonlinearity and an inhomogeneous Dirichlet boundary condition, admitting a nontrivial…
This article carries out a qualitative analysis on a system of integral equations of the Hardy--Sobolev type. Namely, results concerning Liouville type properties and the fast and slow decay rates of positive solutions for the system are…
In this paper, we study the existence of positive non-decreasing radial solutions of a nonlocal non-standard growth problem ruled by the fractional $g$-Laplace operator with exterior Neumann condition. Our argument exploits some properties…
In this short article we obtain some necessary conditions for a so-called fractional Hardy-Sobolev's inequalities in multidimensional case. We also give some examples to show the sharpness of these inequalities.
In this paper, we deal with a fractional elliptic equation with critical Sobolev nonlinearity and Hardy term $$ (-\Delta)^{\alpha} u-\mu\frac{u}{|x|^{2\alpha}}+a(x) u=|u|^{2^*-2}u+k(x)|u|^{q-2}u$$ $$ u\,\in\,H^\alpha({\mathbb R}^N),$$ where…
In this article, we investigate the existence and uniqueness of a positive solution for a class of singular nonlinear elliptic problem with boundary condition. Our result holds in fractional Orlicz-Sobolev spaces.
We investigate the existence and multiplicity of positive solutions to the following problem driven by the superposition of the Laplacian and the fractional Laplacian with Hardy potential \begin{equation*} \left\{ \begin{aligned} -\Delta u…
The aim of this paper is to study a concentration-compactness principle for inhomogeneous fractional Sobolev space $H^s (\mathbb{R}^N)$ for $0<s\leq N/2.$ As an application we establish Palais-Smale compactness for the Lagrangian associated…