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pro vyhledávání: '"Luo, Huxiao"'
Autor:
Xu, Yating, Luo, Huxiao
In this paper, we study the existence of normalized solutions for the nonautonomous Schr\"{o}dinger-Poisson equations \begin{equation}\nonumber -\Delta u+\lambda u +\left(\vert x \vert ^{-1} * \vert u \vert ^{2} \right) u=A(x)|u|^{p-2}u,\quad \text{i
Externí odkaz:
http://arxiv.org/abs/2312.00473
Autor:
Luo, Huxiao, Xu, Meiqing
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), \end{equation*} and the full nonlinear integro-differential equations \b
Externí odkaz:
http://arxiv.org/abs/2312.00469
Autor:
Luo, Huxiao
In this article, we study the Schr\"{o}dinger-Newton equation \begin{equation} -\Delta u+\lambda u=\frac{1}{4\pi}\left(\frac{1}{|x|}\star u^{2}\right)u+|u|^{q-2}u \quad \text{in}~\mathbb{R}^3, \end{equation} where $\lambda\in\mathbb{R}_+$, $q\in (2,3
Externí odkaz:
http://arxiv.org/abs/2312.00465
Autor:
Luo, Huxiao
In this article, we study the uniqueness and nondegeneracy of ground states to a fractional Choquard equation of the form: $(-\Delta)^su+u=2(I_2\star u^2)u$ where $s\in(0,1)$ is sufficiently close to $1$. Our method is to make a continuation argument
Externí odkaz:
http://arxiv.org/abs/2303.14610
Autor:
Luo, Huxiao, Wang, Lushun
In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation: $$-\Delta u-\lambda u=\left(\frac{1}{|x|^{\mu}}\ast A|u|^{p}\right)A|u|^{p-2}u,\quad \int_{\mathbb{R}^{N}}|u|^{2}dx=c,\quad u\in H^1(\mathbb{
Externí odkaz:
http://arxiv.org/abs/2302.05024
We consider the semilinear elliptic equations $$ \left\{ \begin{array}{ll} &-\Delta u+V(x)u=\left(I_\alpha\ast |u|^p\right)|u|^{p-2}u+\lambda u\quad \hbox{for } x\in\mathbb R^N, \\ &u(x) \to 0 \hbox{ as } |x| \to\infty, \end{array} \right. $$ where $
Externí odkaz:
http://arxiv.org/abs/2205.02542
Akademický článek
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Autor:
Luo, Huxiao
Publikováno v:
Discrete & Continuous Dynamical Systems: Series A; Nov2024, Vol. 44 Issue 11, p1-31, 31p
Publikováno v:
Complex Variables & Elliptic Equations; Aug2024, Vol. 69 Issue 8, p1412-1436, 25p