In:
Topological Methods in Nonlinear Analysis, Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University, ( 2023-09-23), p. 1-14
Abstract:
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 $\lambda_j$, $j=1,\ldots,N$.
Type of Medium:
Online Resource
ISSN:
1230-3429
DOI:
10.12775/TMNA.2022.071
Language:
Unknown
Publisher:
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Publication Date:
2023
detail.hit.zdb_id:
2043491-1
SSG:
17,1
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