|
| 摘要: |
| 本文考虑了以下混合色散非线性~Schr\"odinger~方程
\begin{equation*}\label{eq0}
\Delta^{2}u-\beta\Delta u-\frac{\lambda}{2}\Delta(u^{2})u=g(u),\quad\,\, x\in\mathbb{R}^{N}.\tag{0.1}
\end{equation*}
其中~$g:\mathbb{R}\rightarrow\mathbb{R}$~是一个连续函数, $\lambda\geq 0$, $\beta\geq 0$. 由于~Sobolev~嵌入的不同, 我们对~$N=4$~的情况感兴趣. 并且在四阶色散项和拟线性项的影响下, 利用变分法证明了方程~\eqref{eq0}无穷多非径向解的存在性. |
| 关键词: 多重性 非径向解 拟线性问题 四阶算子 |
| DOI： |
| 分类号:35J35, 35J60, 35J62 |
| 基金项目: |
|
| Multiple non-radial solutions to a mixed dispersion nonlinear Schr\"odinger equation |
|
He Juhua
|
| Abstract: |
| We consider the following mixed dispersion nonlinear Schr\"odinger equation
\begin{equation}\label{eq0}
\Delta^{2}u-\beta\Delta u-\frac{\lambda}{2}\Delta(u^{2})u=g(u)\quad\,\, \text{in}\,\,\mathbb{R}^{N},
\end{equation}
where $g:\mathbb{R}\rightarrow\mathbb{R}$ is a continuous function, $\lambda\geq 0$, $\beta\geq 0$. Due to the differences in Sobolev embedding, we are interested in the case $N=4$. And under the influence of fourth-order dispersion and quasilinear terms, we shall prove that ~\eqref{eq0} has multiple non-radial solutions by variational method. |
| Key words: Multiplicity Non-radial solutions Quasilinar problem Fourth-order operator |
