46 citations · 137 across the 27 of their papers we have counts for
6 papers · 1 filter
Singularly perturbed critical Choquard equations
Claudianor O. Alves, Fashun Gao, Marco Squassina +1
In this paper we study the semiclassical limit for the singularly perturbed Choquard equation $$ -\vr^2Δu +V(x)u =\vr^{μ-3}\Big(\int_{\R^3} \frac{Q(y)G(u(y))}{|x-y|^μ}dy\Big)Q(x)g(…
On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents
Fashun Gao, Minbo Yang
We consider the following nonlinear Choquard equation with Dirichlet boundary condition $$-Δu =\left(\int_Ω\frac{|u|^{2_μ^{\ast}}}{|x-y|^μ}dy\right)|u|^{2_μ^{\ast}-2}u+λf(u)\hspace…
Stability and instability of standing waves for a generalized Choquard equation with potential
Zhipeng Cheng, Minbo Yang
We are going to study the standing waves for a generalized Choquard equation with potential: $$ -i\partial_t u-Δu+V(x)u=(|x|^{-μ}\ast|u|^p)|u|^{p-2}u, \ \ \hbox{in}\ \ \mathbb{R}\t…
Multi-peak solutions for nonlinear Choquard equation with a general nonlinearity
Minbo Yang, Jianjun Zhang, Yimin Zhang
In this paper, we study a class of nonlinear Choquard type equations involving a general nonlinearity. By using the method of penalization argument, we show that there exists a fam…
On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation
Fashun Gao, Minbo Yang
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation $$-Δu =\left(\int_Ω\frac{|u|^{2_μ^{\ast}}}{|x-y|^μ}dy\right)|u|^{2_μ^{\…
Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in
Claudianor O. Alves, Daniele Cassani, Cristina Tarsi +1
We study the following singularly perturbed nonlocal Schrödinger equation $$ -\vr^2Δu +V(x)u =\vr^{μ-2}\Big[\frac{1}{|x|^μ}\ast F(u)\Big]f(u) \quad \mbox{in} \quad \R^2, $$ where $…