论文标题
通用混合分散NLS方程的径向和非radial多重溶液
Radial and non-radial multiple solutions to a general mixed dispersion NLS equation
论文作者
论文摘要
We study the following nonlinear Schrödinger equation with a forth order dispersion term \[ Δ^2u-βΔu=g(u) \quad \text{in } \mathbb{R}^N \] in the positive and zero mass regimes: in the former, $N\geq 2$ and $β> -2\sqrt{m}$, where $m>0$ depends on $ g $;在后者中，$ n \ geq 3 $和$β> 0 $。在这两个制度中，我们在大约$ g $的相当通用假设下找到了无限的解决方案序列；如果$ n = 2 $在正质量案例中，或零质量案例中的$ n = 4 $，我们需要加强此类假设。我们的方法是变异的。
We study the following nonlinear Schrödinger equation with a forth order dispersion term \[ Δ^2u-βΔu=g(u) \quad \text{in } \mathbb{R}^N \] in the positive and zero mass regimes: in the former, $N\geq 2$ and $β> -2\sqrt{m}$, where $m>0$ depends on $g$; in the latter, $N\geq 3$ and $β>0$. In either regimes, we find an infinite sequence of solutions under rather generic assumptions about $g$; if $N=2$ in the positive mass case, or $N=4$ in the zero mass case, we need to strengthen such assumptions. Our approach is variational.
