论文标题
紧凑的嵌入定理和狮子型引理分数orlicz-sobolev空间
Compact embedding theorems and a Lions' type Lemma for fractional Orlicz-Sobolev spaces
论文作者
论文摘要
在本文中，我们关注有关分数Orlicz-Sobolev空间的一些抽象结果。确切地说，我们确保加权分数Orlicz-Sobolev空间的紧凑性嵌入到Orlicz空间中，前提是重量不受限制。我们还通过引入新技术来克服缺乏合适的插值定律，从而为分数Orlicz-Sobolev空间获得狮子的“消失”引理版本。最后，作为抽象结果的乘积，我们使用尼哈里歧管上的最小化方法来证明一类非线性schrödinger方程的基态解决方案的存在，同时考虑了无界或有限的潜力。
In this paper we are concerned with some abstract results regarding to fractional Orlicz-Sobolev spaces. Precisely, we ensure the compactness embedding for the weighted fractional Orlicz-Sobolev space into the Orlicz spaces, provided the weight is unbounded. We also obtain a version of Lions' "vanishing" Lemma for fractional Orlicz-Sobolev spaces, by introducing new techniques to overcome the lack of a suitable interpolation law. Finally, as a product of the abstract results, we use a minimization method over the Nehari manifold to prove the existence of ground state solutions for a class of nonlinear Schrödinger equations, taking into account unbounded or bounded potentials.
