论文标题
涉及分数$ g $ -laplacian的问题，缺乏紧凑
Problems involving the fractional $g$-Laplacian with Lack of Compactness
论文作者
论文摘要
在本文中，我们证明了分数orlicz-sobolev space的子空间的紧凑嵌入$ w^{s，g} \ left（\ mathbb {r}^{n} \ right）$由径向函数组成的$，我们的目标嵌入空间是Orlicz型的。另外，我们证明了$ w^{s，g} \ left（\ mathbb {r}^{n} \ right）$的狮子和LIEB类型结果，该$以一种特定的方式可以获得弱极限为非平底的序列。作为一个应用程序，我们研究了整个空间中准线性椭圆问题的解决方案$ \ mathbb {r}^n $，涉及分数$ g- $ laplacian操作员，其中共轭函数$ \ widetilde {g widetilde {g} $ g $ of $ g $不满足$δ_2$ - $ condition。
In this paper we prove compact embedding of a subspace of the fractional Orlicz-Sobolev space $W^{s, G}\left(\mathbb{R}^{N}\right)$ consisting of radial functions, our target embedding spaces are of Orlicz type. Also, we prove a Lions and Lieb type results for $W^{s,G}\left(\mathbb{R}^{N}\right)$ that works together in a particular way to get a sequence whose the weak limit is nontrivial. As an application, we study the existence of solutions to Quasilinear elliptic problems in the whole space $\mathbb{R}^N$ involving the fractional $g-$Laplacian operator, where the conjugated function $\widetilde{G}$ of $G$ doesn't satisfy the $Δ_2$-condition.
