6 papers
Normalized solutions for nonautonomous Schrödinger-Poisson equations
Yating Xu, Huxiao Luo
In this paper, we study the existence of normalized solutions for the nonautonomous Schrödinger-Poisson equations \begin{equation}\nonumber -Δu+λu +\left(\vert x \vert ^{-1} * \ver…
Maximum principles for nonlinear integro-differential equations and symmetry of solutions
Huxiao Luo, Meiqing Xu
In this paper, we study the semilinear integro-differential equations \begin{equation*} \mathcal{L}_{K}u(x)\equiv C_n\text{P.V.}\int_{\R^n}\left(u(x)-u(y)\right)K(x-y)dy=f(x,u), \e…
Uniqueness and nondegeneracy of ground states for the Schrödinger-Newton equation with power nonlinearity
Huxiao Luo
In this article, we study the Schrödinger-Newton equation \begin{equation} -Δu+λu=\frac{1}{4π}\left(\frac{1}{|x|}\star u^{2}\right)u+|u|^{q-2}u \quad \text{in}~\mathbb{R}^3, \end{e…
Uniqueness and nondegeneracy of ground states for in when is close to 1
Huxiao Luo
In this article, we study the uniqueness and nondegeneracy of ground states to a fractional Choquard equation of the form: where is suffici…
Normalized ground states solutions for nonautonomous Choquard equations
Huxiao Luo, Lushun Wang
In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation: $$-Δu-λu=\left(\frac{1}{|x|^μ}\ast A|u|^{p}\right)A|u|^{p-2}u,\quad \in…
Bifurcation into spectral gaps for strongly indefinite Choquard equations
Huxiao Luo, Bernhard Ruf, Cristina Tarsi
We consider the semilinear elliptic equations $$ \left\{ \begin{array}{ll} &-Δu+V(x)u=\left(I_α\ast |u|^p\right)|u|^{p-2}u+λu\quad \hbox{for } x\in\mathbb R^N, \\ &u(x) \to 0 \hbox…