Description

• Title:
  Multiple nodal solutions for a critical nonlinear Choquard equation
• Creator:
  Barboza, Eudes Mendes;
  Miyagaki, Olímpio H.;
  Santana, Claudia R.
• Description:
  In this paper, our goal is to investigate the existence of multiple nodal solutions to the following class of problems \begin{equation*} \begin{cases} -\Delta u+ V(x) u = \big(I_{\alpha}\ast |u|^{2_{\alpha}^* }\big) |u|^{2_{\alpha}^* -2}u +\lambda g(u) & \text{in } \mathbb{R}^N,\\ u \in H^1(\mathbb{R}^N), \end{cases} \end{equation*} where $I_{\alpha}$ represents the Riesz potential, $V$ is a continuous potential, $N\geq 3$, $0< \alpha< N$, $\lambda> 0$, $2^*_{\alpha}= ({N+\alpha})/({N-2})$ is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality and $g$ is a local or nonlocal superlinear perturbation with subcritical growth in the sense of Sobolev or Hardy-Littlewood-Sobolev, respectively. For this matter, combining variational methods with the technique introduced in \cite{primeiro}, which was adapted for Choquard equations in \cite{GuiGuo}, \cite{nodal}, we show that for any positive $k\in \mathbb{N}$ the previous problem with a nonlinearity involving critical growth has at least a radially symmetrical ground state solution changing sign exactly $k$-times.
• Object availability:
  free access
• Date:
  2025.06.14
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Online First Articles; 1 - 34;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/62302/42805 ;https://apcz.umk.pl/TMNA/article/view/62302/42806
• Subject:
  Choquard equation;
  critical Hardy-Littlewood-Sobolev Growth;
  nodal solutions;
  variational problems;
  critical points;
  Primary: 35J20, 35B33;
  Secondary: 35B34, 35B38, 35R11
• Identifier: https://apcz.umk.pl/TMNA/article/view/62302
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other