论文标题
存在$ \ mathbb {r} $中的分数choquard-type方程的解决方案，并具有关键的指数增长
Existence of solutions for a fractional Choquard--type equation in $\mathbb{R}$ with critical exponential growth
论文作者
论文摘要
在本文中，我们研究了以下类别的类别choquard-type方程\ [（ - δ）^{1/2} u + + u = \ big（i_μ\ ast f（u）\ big）\ big）f（u），\ quad x \ in \ in \ mathbb {r}，r}，\ r}，\]，$（ - Δ）运营商，$i_μ$是$ 0 <μ<1 $，$ f $的Riesz潜力，是$ f $的原始功能。当$ F $在Trudinger-Moser不平等方面具有关键的指数增长时，我们使用变分方法和最小值估计来研究解决方案的存在。
In this paper we study the following class of fractional Choquard--type equations \[ (-Δ)^{1/2}u + u=\Big( I_μ\ast F(u)\Big)f(u), \quad x\in\mathbb{R}, \] where $(-Δ)^{1/2}$ denotes the $1/2$--Laplacian operator, $I_μ$ is the Riesz potential with $0<μ<1$ and $F$ is the primitive function of $f$. We use Variational Methods and minimax estimates to study the existence of solutions when $f$ has critical exponential growth in the sense of Trudinger--Moser inequality.
