Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Concentrating bounded states for fractional Schrödinger-Poisson system involving critical Sobolev exponent (1906.10802v1)

Published 26 Jun 2019 in math.AP

Abstract: In this paper, we study the concentration and multiplicity of solutions to the following fractional Schr\"{o}dinger-Poisson system \begin{equation*} \left{ \begin{array}{ll} \varepsilon{2s}(-\Delta)su+V(x)u+\phi u=f(u)+u{2_s{\ast}-1} & \hbox{in $\mathbb{R}3$,} \varepsilon{2t}(-\Delta)t\phi=u2, u>0& \hbox{in $\mathbb{R}3$,} \end{array} \right. \end{equation*} where $s>\frac{3}{4}$, $s,t\in(0,1)$, $\varepsilon>0$ is a small parameter, $f\in C1(\mathbb{R}{+},\mathbb{R})$ is subcritical, $V:\mathbb{R}3\rightarrow\mathbb{R}$ is a continuous bounded function. We establish a family of positive solutions $u_{\varepsilon}\in H_{\varepsilon}$ which concentrates around the local minima of $V$ in $\Lambda$ as $\varepsilon\rightarrow0$. With Ljusternik-Schnirelmann theory, we also obtain multiple solutions by employing the topology construct of the set where the potential $V$ attains its minimum.

Summary

We haven't generated a summary for this paper yet.