Existence and asymptotic behavior for the ground state of quasilinear elliptic equation
Xiaoyu Zeng, Yimin Zhang · arXiv (Cornell University) · 2017
In this paper, we are concerned with the existence and asymptotic behavior of minimizers for a minimization problem related to some quasilinear elliptic equations. Firstly, we proved that there exist minimizers when the exponent $q$ equals to the critical case $q^*=2+\frac{4}{N}$, which is different from that of \cite{cjs}. Then, we proved that all minimizers are compact as $q$ tends to the critical case $q^*$ when $aa^*$.