Description

• Title:
  Multiple Normalized Solutions for Choquard equations involving Kirchhoff type perturbation
• Creator:
  Liu, Zeng
• Description:
  In this paper we study the existence of critical points of the $C^1$ functional \begin{equation*} E(u)=\frac{a}{2}\int_{\bbrn}|\nabla u|^2dx+\frac{b}{4}\bigg(\int_{\bbrn}|\nabla u|^2dx\bigg)^2-\frac{1}{2p}\int_{\bbrn}(I_\alpha*|u|^p)|u|^pdx \end{equation*} under the constraint \begin{equation*} S_c=\bigg\{u\in H^1(\bbrn)\ \bigg\vert\ \int_{\bbrn}|u|^2dx=c^2\bigg\}, \end{equation*} where $a> 0$, $b> 0$, $N\geq3$, $\alpha\in(0,N)$, $ (N+\alpha)/{N}< p< (N+\alpha)/$ $(N-2)$ and $I_{\alpha}$ is the Riesz Potential. When $p$ belongs to different ranges, we obtain the threshold values separating the existence and nonexistence of critical points of $E$ on $S_c$. We also study the behaviors of the Lagrange multipliers and the energies corresponding to the constrained critical points when $c\to 0$ and $c\to +\infty$, respectively.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.07.21
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 1 (September 2019); 297 - 319;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.046/18029 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.046/18030
• Subject:
  Choquard equation;
  Kirchhoff equation;
  mountain pass geometry;
  normalized solutions;
  35J61;
  35M10;
  35J20;
  35B40
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.046
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other