相关论文: Choquard equations with critical exponential nonli…
In this paper we study the Nirenberg problem on standard half spheres $(\mathbb{S}^n_+,g), \, n \geq 5$, which consists of finding conformal metrics of prescribed scalar curvature and zero boundary mean curvature on the boundary. This…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
We study the Choquard equation involving mixed local and nonlocal operators \[-\varepsilon^{2}\Delta u+\varepsilon^{2s}(-\Delta)^{s}u+V(x)u=\varepsilon^{\mu-2}\left(\frac{1}{|x|^{\mu}}*F(u)\right)f(u)\quad \text{in }\R^{2},\] where…
We prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, i.e. solutions of the Einstein vacuum equations for asymptotically flat $1+3$ dimensional Lorentzian metrics which admit a…
This paper is focused on the solvability of a family of nonlinear elliptic systems defined in $\mathbb{R}^N$. Such equations contain Hardy potentials and Hardy-Sobolev criticalities coupled by a possible critical Hardy-Sobolev term. That…
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These…
In this paper we study the existence of solutions and their concentration phenomena of a singularly perturbed semilinear Schrodinger equation with the presence of the critical Sobolev exponent.
The purpose of this paper is to extend the embedding theorem of Sobolev spaces involving general kernels and we provide a sharp critical exponent in these embeddings. As an application, solutions for equations driven by a general…
The aim of this work is to prove a compact embedding for a weighted fractional Sobolev spaces. As an application, we use this embedding to prove, via variational methods, the existence of solutions for the following Schr\"odinger equation…
We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the…
Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case $q \in (0,1)$ $$\displaystyle \ \ -\Delta u+ u =I_\alpha[u^p] u^q\;\; {\rm in}\; \mathbb{R}^N\setminus\{0\}, %…
This paper deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. When the poles form a symmetric structure, it is natural we wonder…
This paper deals with existence and multiplicity of positive solutions for a quasilinear problem with Neumann boundary conditions, set in a ball. The problem admits at least one constant non-zero solution and it involves a nonlinearity that…
In this paper, we study the nonlocal Choquard equation $$ -\varepsilon^2 \Delta u_\varepsilon + V u_\varepsilon= (I_\alpha * |u_\varepsilon|^p)|u_\varepsilon|^{p-2}u_\varepsilon $$ where $N\geq 1$, $I_\alpha$ is the Riesz potential of order…
We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…
In this paper we study the existence of radially symmetric solitary waves in R^N for the nonlinear Klein-Gordon equations coupled with the Maxwell's equations when the nonlinearity exhibits critical growth. The main feature of this kind of…
We consider the following doubly nonlocal nonlinear logistic problem driven by the fractional $p$-Laplacian \begin{equation*} \pl u = f(x,u) -\cq ~\text{in}~ \O, ~u=0 ~\text{in}~ \Rn\setminus\O. \end{equation*} Here $ \O \subset \Rn…
We study the existence of normalized solutions to the following Choquard equation with $F$ being a Berestycki-Lions type function \begin{equation*} \begin{cases} -\Delta u+\lambda u=(I_{\alpha}\ast F(u))f(u),\quad \text{in}\ \mathbb{R}^N,…
The aim of this work is to study the numerical solution of the nonlinear Schrodinger problem using a combination between Witt basis and finite difference approximations. We construct a discrete fundamental solution for the non-stationary…
We study the stochastic nonlinear Schroedinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy-critical cases. For general initial data, we prove the global existence and uniqueness of…