Description

• Title:
  Fractional Kirchhoff-Schrödinger equation with critical exponential growth in $\mathbb{R}^{N}$
• Creator:
  Liu, Yanjun;
  Yin, Lifeng
• Description:
  In this paper, we consider the following fractional Kirchhoff-Schrödinger equation: \begin{equation*} \begin{cases} \displaystyle \Big(a+b\|u\|_{E}^{p(\theta-1)}\Big) \big[(-\triangle)_{p}^{s}u+V(x)|u|^{p-2}u\big]=f(x, u), & x \in \mathbb{R}^{N},\\ \noalign{\vskip5pt} \displaystyle \|u\|_{E}^p:=\iint_{\mathbb{R}^{2N}} \frac{|u(x)-u(y)|^{p}}{|x-y|^{N+sp}}dxdy +\int_{\mathbb{R}^{N}}V(x)|u|^{p}dx, \end{cases} \end{equation*} where $a> 0$, $b \geq 0$, $\theta \geq1$, dimension $N=sp$ with $s \in (0, 1)$ and $p\geq 1$. $ V$ is a positive potential and $f$ is a critical nonlinearity with exponential growth. We derive a positive ground state solution by using minimax techniques combined with the fractional Truding-Moser inequality. Moreover, in the particular case of $a=1$ and $b=0$, we also obtain the existence of the ground state solution to the fractional Schrödinger equation.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.02.10
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 1 (March 2021); 275 - 295;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.030/28172 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.030/28173
• Subject:
  Fractional Kirchhoff-Schrödinger;
  critical exponential growth;
  fractional Trudinger-Moser inequality;
  the ground state solution;
  Primary;
  35A15;
  35R11;
  Secondary;
  47G20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.030
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other