Existence of solutions for a class of Kirchhoff-type equations with indefinite potential
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913288390967296 |
|---|---|
| author | Xiao, Linlian Yuan, Jiaqian Zhou, Jian Wu, Yunshun |
| author_facet | Xiao, Linlian Yuan, Jiaqian Zhou, Jian Wu, Yunshun |
| contents | In this paper, we consider the existence of solutions of the following Kirchhoff-type problem \[
\left\{
\begin{array}
[c]{ll}
-\left(a+b\int_{\mathbb{R}^3}|\nabla u|^2dx\right)Δu+ V(x)u=f(x,u),~{\rm{in}}~ \mathbb{R}^{3},\\
u\in H^1(\mathbb{R}^3),
\end{array} \right. \] where $a,b$ are postive constants, and the potential $V(x)$ is continuous and indefinite in sign. Under some suitable assumptions on $V(x)$ and $f$, we obtain the existence of solutions by the Symmetric Mountain Pass Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of solutions for a class of Kirchhoff-type equations with indefinite potential Xiao, Linlian Yuan, Jiaqian Zhou, Jian Wu, Yunshun Analysis of PDEs In this paper, we consider the existence of solutions of the following Kirchhoff-type problem \[ \left\{ \begin{array} [c]{ll} -\left(a+b\int_{\mathbb{R}^3}|\nabla u|^2dx\right)Δu+ V(x)u=f(x,u),~{\rm{in}}~ \mathbb{R}^{3},\\ u\in H^1(\mathbb{R}^3), \end{array} \right. \] where $a,b$ are postive constants, and the potential $V(x)$ is continuous and indefinite in sign. Under some suitable assumptions on $V(x)$ and $f$, we obtain the existence of solutions by the Symmetric Mountain Pass Theorem. |
| title | Existence of solutions for a class of Kirchhoff-type equations with indefinite potential |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.19284 |