Description

• Title:
  Multiplicity of positive solutions for a Kirchhoff type problem without asymptotic conditions
• Creator:
  Qian, Xiaotao
• Description:
  In this paper, we are concerned with the multiplicity of positive solutions for the following Kirchhoff type problem \[ \begin{cases} -\bigg({\varepsilon}^2a+{\varepsilon}b\int_{\mathbb{R}^3} |\n u|^2dx\bigg)\Delta u+u=Q(x)|u|^{p-2}u, & x\in\mathbb{R}^3,\\ u\in H^1\big(\mathbb{R}^3\big), \quad u> 0, & x\in\mathbb{R}^3, \end{cases} \] where $\varepsilon> 0$ is a small parameter, $a,b> 0$ are constants, $4< p< 6$, $Q$ is a nonnegative continuous potential and does not satisfy any asymptotic condition. Combining Nehari manifold and concentration compactness principle, we study how the shape of the graph of $Q(x)$ affects the number of positive solutions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2023 Xiaotao Qian;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2023.06.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 61, No 2 (June 2023); 681 - 700;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/44692/35873 ;https://apcz.umk.pl/TMNA/article/view/44692/35874
• Subject:
  Kirchhoff type problem;
  multiple positive solutions;
  variational methods;
  35J20, 35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/44692
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other