Description

• Title:
  Liouville type theorems for Kirchhoff sub-elliptic equations involving $\Delta_\lambda$-operators
• Creator:
  Nguyen, Thi Thu Huong;
  Quyet, Dao Trong;
  Vu, Thi Hien Anh
• Description:
  In this paper, we study the Kirchhoff elliptic equations of the form $$ -M(\|\nabla_\lambda u\|^2)\Delta_\lambda u=w(x)f(u) \quad \mbox{in }\mathbb R^{N}, $$ where $M$ is a smooth monotone function, $w$ is a weight function and $f(u)$ is of the form $u^p, e^u$ or $-u^{-p}$. The operator $\Delta_\lambda$ is strongly degenerate and given by $$ \Delta_\lambda=\sum_{j=1}^N \frac{\partial}{\partial x_j}\bigg(\lambda_j^2(x)\frac{\partial }{\partial x_j}\bigg). $$ We shall prove some classifications of stable solutions to the equation above under general assumptions on $M$ and $\lambda_j$, $j=1,\ldots,N$.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Thi Thu Huong Nguyen, Dao Trong Quyet, Thi Hien Anh Vu
• 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); 327 - 340;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/46314/36565 ;https://apcz.umk.pl/TMNA/article/view/46314/36566
• Subject:
  Liouville type theorems;
  $\Delta_\lambda$-Laplacian;
  stable solutions;
  Kirchhoff equations;
  Primary: 35B53, 35J60;
  Secondary: 35B35
• Identifier: https://apcz.umk.pl/TMNA/article/view/46314
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other