| |
| In this paper, we consider the existence and non-existence of non-trivial solution to a Brezis-Nirenberg type problem with singular weights.
First, we obtain a compact imbedding theorem which is an extension of the classical Rellich-Kondrachov compact imbedding theorem, and consider the corresponding eigenvalue problem.
Secondly, we deduce a Pohozaev type identity and obtained a non-existence result.
Thirdly, based on a
generalized concentration compactness principle, we will give some
abstract conditions when the functional satisfies the (PS)$_c$
condition. Finally, based on the explicit form of the extremal function, we will obtain some existence results to the problem.
|
|
| Keywords:Brezis-Nirenberg problem, singular weights |
|
