Related papers: Higher nonlocal problems with bounded potential
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…
This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We establish the existence of infinitely many nontrivial weak…
Our concern in this paper is to study the qualitative properties for harmonic functions related to the fractional Laplacian. Firstly we classify the polynomials in the whole space and in the half space for the fractional Laplacian defined…
In this paper, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classical hyperelasticity, aiming for an effective framework to…
In this paper we analyze an eigenvalue problem related to the nonlocal $p-$laplace operator plus a potential. After reviewing some elementary properties of the first eigenvalue of these operators (existence, positivity of associated…
We study the formation of localized modes around a generalized nonlinear impurity which is located at the boundary of a semi-infinite square lattice, and where we replace the standard discrete Laplacian by a fractional one, characterized by…
We present explicit formulas for solutions to nonhomogeneous boundary value problems involving any positive power of the Laplacian in the half-space. For non-integer powers the operator becomes nonlocal and this requires a suitable…
In the present work we study existence of sequences of variational eigenvalues to non-local non-standard growth problems ruled by the fractional $g-$Laplacian operator with different boundary conditions (Dirichlet, Neumann and Robin). Due…
The main goal is to establish necessary and sufficient conditions under which the fractional semilinear elliptic equation $\Delta^{\frac{\alpha}{2}} u=\rho(x)\,\varphi(u)$ admits nonnegative nontrivial bounded solutions in the whole space…
We discuss tangential Sobolev-estimates up to the boundary for solutions to the regional fractional laplacian on the upper half-plane. These estimates can be used to reduce the boundary Calderon-Zygmund theory of any dimension to a…
In this paper we prove the existence of a positive solution of the nonlinear and nonlocal elliptic equation in $\mathbb{R}^n$ \[ (-\Delta)^s u =\varepsilon h u^q+u^{2_s^*-1} \] in the convex case $1\leq q<2_s^*-1$, where $…
This article is mainly devoted to the asymptotic analysis of a fractional version of the (elliptic) Allen-Cahn equation in a bounded domain $\Omega\subset\mathbb{R}^n$, with or without a source term in the right hand side of the equation…
We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type $$\big(\Phi(k(t)\,x'(t))\big)' + f(t,\mathcal{G}_x(t))\,\rho(t, x'(t)) = 0$$ on a compact interval $[a,b]$.…
In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains.
The purpose of this paper is to study the existence of weak solutions for some classes of hemivariational problems in the Euclidean space $\mathbb{R}^d$ ($d\geq 3$). These hemivariational inequalities have a variational structure and,…
We prove the nondegeneracy of the extremals of the fractional Sobolev inequality as solutions of a critical semilinear nonlocal equation involving the fractional Laplacian.
This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More precisely, the existence of at least two non-trivial weak (strong) solutions for the…
In this article, we study the following fractional $p$-Laplacian equation with critical growth singular nonlinearity \begin{equation*} \quad (-\De_{p})^s u = \la u^{-q} + u^{\alpha}, u>0 \; \text{in}\; \Om,\quad u = 0 \; \mbox{in}\; \mb R^n…
In this paper, we study a class of semilinear nonlocal elliptic equations posed on settings without compact Sobolev embedding. More precisely, we prove the existence of infinitely many solutions to the fractional Brezis-Nirenberg problems…
We show that solutions of nonlinear nonlocal Fokker--Planck equations in a bounded domain with no-flux boundary conditions can be approximated by Cauchy problems with increasingly strong confining potentials defined in the whole space. Two…