Description

• Title:
  Three positive solutions for the indefinite fractional Schrödinger-Poisson systems
• Creator:
  Che, Guofeng;
  Wu, Tsung-fang
• Description:
  In this paper, we are concerned with the following fractionalSchrödinger-Poisson systems with concave-convex nonlinearities: \begin{equation*} \begin{cases} (-\Delta )^{s}u+u+\mu l(x)\phi u=f(x)|u|^{p-2}u+g(x)|u|^{q-2}u& \text{in }\mathbb{R}^{3}, \\ (-\Delta )^{t}\phi =l(x)u^{2} & \text{in }\mathbb{R}^{3},% \end{cases} \end{equation*} where ${1}/{2}< t\leq s< 1$, $1< q< 2< p< \min \{4,2_{s}^{\ast }\}$, $2_{s}^{\ast }={6}/({3-2s})$, and $\mu > 0$ is a parameter, $f\in C\big(\mathbb{R}^{3}\big)$ is sign-changing in $\mathbb{R}^{3}$ and $g\in L^{p/(p-q)}\big(\mathbb{R}^{3}\big)$. Under some suitable assumptions on $l(x)$, $f(x)$ and $g(x)$, we explore that the energy functional corresponding to the system is coercive and bounded below on $H^{\alpha }\big(\mathbb{R}^{3}\big)$ which gets a positive solution. Furthermore, we constructed some new estimation techniques, and obtained other two positive solutions. Recent results from the literature are generally improved and extended.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Guofeng Che, Tsung-fang Wu
• Date:
  2023.09.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 62, No 1 (September 2023); 53 - 81;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/46305/36547 ;https://apcz.umk.pl/TMNA/article/view/46305/36548
• Subject:
  Fractional Schrödinger-Poisson systems;
  Nehari manifold;
  multiple positive solutions;
  variational methods;
  Primary: 35B38;
  Secondary: 35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/46305
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other