论文标题
与合并非线性的$ \ mathbb {r}^n $中的一类分数schrödinger方程的无限解决方案存在
Existence of infinitely many solutions for a class of fractional Schrödinger equations in $\mathbb{R}^N$ with combined nonlinearities
论文作者
论文摘要
本文专用于以下非线性分数schrödinger方程：\ begin {equination*}（-Δ） （0,1）$，$ n> 2s $，$（δ）^{s} $代表分数laplacian，$λ\ in \ mathbb {r} $是一个参数，$ v \ in c（\ mathbb {r}^n，r}^n，r） $ u $。我们通过喷泉定理证明了上述方程的许多高能解决方案的存在。最近的一些结果得到了扩展并大幅改善。
This paper is devoted to the following class of nonlinear fractional Schrödinger equations: \begin{equation*} (-Δ)^{s} u + V(x)u = f(x,u) + λg(x,u), \quad \text{in}\: \mathbb{R}^N, \end{equation*} where $s\in (0,1)$, $N>2s$, $(-Δ)^{s}$ stands for the fractional Laplacian, $λ\in \mathbb{R}$ is a parameter, $V\in C(\mathbb{R}^N,R)$, $f(x,u)$ is superlinear and $g(x,u)$ is sublinear with respect to $u$, respectively. We prove the existence of infinitely many high energy solutions of the aforementioned equation by means of the Fountain theorem. Some recent results are extended and sharply improved.
