论文标题
紧凑的嵌入，特征值问题和下去brezis-nirenberg方程，涉及分层谎言组的奇异性
Compact Embeddings, Eigenvalue Problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups
论文作者
论文摘要
本文的目的是双重的：首先，我们研究了分数folland-stein-sobolev空间在分层的谎言组上的分数$ p $ -sub-laplacian的特征值问题。我们采用各种方法来研究特征值问题。我们通过强大的最低原理的分数$ p $ -sub-sub-laplacian来得出结论第一个本征功能的积极性。此外，我们推断出第一个特征值简单而孤立。其次，利用已建立的属性，我们通过nehari歧管技术证明了至少两种弱解决方案，以与分层lie群上的一类与分数$ p $ -sub-sub-laplacian相关的小细胞奇异问题。我们还通过MOSER迭代技术研究了积极弱解针对所考虑的问题的界限。即使对于Case $ P = 2 $，此处获得的结果也是新的，而Mathbb {G} $作为Heisenberg Group。
The purpose of this paper is twofold: first we study an eigenvalue problem for the fractional $p$-sub-Laplacian over the fractional Folland-Stein-Sobolev spaces on stratified Lie groups. We apply variational methods to investigate the eigenvalue problems. We conclude the positivity of the first eigenfunction via the strong minimum principle for the fractional $p$-sub-Laplacian. Moreover, we deduce that the first eigenvalue is simple and isolated. Secondly, utilising established properties, we prove the existence of at least two weak solutions via the Nehari manifold technique to a class of subelliptic singular problems associated with the fractional $p$-sub-Laplacian on stratified Lie groups. We also investigate the boundedness of positive weak solutions to the considered problem via the Moser iteration technique. The results obtained here are also new even for the case $p=2$ with $\mathbb{G}$ being the Heisenberg group.
