一类约束变分问题极小元的存在性及其集中行为

The Existence of Minimizers for a Class of Constrained Variational Problem with Its Concentration Behavior

该文主要讨论了一类带有调和位势p-Laplacian方程特征值问题对应的变分泛函极小元的存在性与非存在性,并且使用能量估计的方法分析了当方程中相关参数逼近其临界值时极小元的集中行为.

In this paper, we mainly discuss the existence and non-existence of minimizers for the variational functional of a p-Laplacian eigenvalue problem involving harmonic potential. Moreover, the concentration behavior of the minimizers is also investigated by using the energy method when the related parameter closes to a critical value.