Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11693 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909567975161856 |
|---|---|
| author | Filho, Antônio de Pádua Farias de Souza |
| author_facet | Filho, Antônio de Pádua Farias de Souza |
| contents | We investigate the following Kirchhoff-type biharmonic equation \begin{equation}\label{pr} \left\{ \begin{array}{ll} Δ^2 u+ \left(a+b\int_{\mathbb{R}^N}|\nabla u|^2d x\right)(-Δu+V(x)u)=f(x,u),\quad x\in \mathbb{R}^N,\\ u\in H^{2}(\mathbb{R}^N), \end{array} \right. \end{equation} where $a>0$, $b\geq 0$ and $V(x)$ and $f(x, u)$ are periodic or asymptotically periodic in $x$. We study the existence of Nehari-type ground state solutions of the problem just above with $f(x,u)u-4F(x,u)$ sign-changing, where $F(x,u):=\int_0^uf(x,s)d s$. We significantly extend some results from the previous literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nehari-type ground state solutions for asymptotically periodic bi-harmonic Kirchhoff-type problems in $\mathbb{R}^N$ Filho, Antônio de Pádua Farias de Souza Analysis of PDEs 35G20, 35J10, 35J30, 35J35 We investigate the following Kirchhoff-type biharmonic equation \begin{equation}\label{pr} \left\{ \begin{array}{ll} Δ^2 u+ \left(a+b\int_{\mathbb{R}^N}|\nabla u|^2d x\right)(-Δu+V(x)u)=f(x,u),\quad x\in \mathbb{R}^N,\\ u\in H^{2}(\mathbb{R}^N), \end{array} \right. \end{equation} where $a>0$, $b\geq 0$ and $V(x)$ and $f(x, u)$ are periodic or asymptotically periodic in $x$. We study the existence of Nehari-type ground state solutions of the problem just above with $f(x,u)u-4F(x,u)$ sign-changing, where $F(x,u):=\int_0^uf(x,s)d s$. We significantly extend some results from the previous literature. |
| title | Nehari-type ground state solutions for asymptotically periodic bi-harmonic Kirchhoff-type problems in $\mathbb{R}^N$ |
| topic | Analysis of PDEs 35G20, 35J10, 35J30, 35J35 |
| url | https://arxiv.org/abs/2501.11693 |