Title: On the behavior of the ground state energy under weak perturbation of critical quasilinear operators in $\mathbb{R}^N$ Show Chinese title

Title: 在临界拟线性算子的弱扰动下基态能量的行为在$\mathbb{R}^N$中

Abstract: We consider a critical quasilinear operator $-\Delta_p u +V|u|^{p-2}u$ in $\mathbb{R}^N$ perturbed by a weakly coupled potential. For $N>p$, we find the leading asymptotic of the lowest eigenvalue of such an operator in the weak coupling limit separately for $N>p^2$ and $N\leq p^2$. Show Chinese abstract

Abstract: 我们考虑一个临界拟线性算子$-\Delta_p u +V|u|^{p-2}u$在$\mathbb{R}^N$中受弱耦合势的扰动。对于$N>p$，我们在弱耦合极限下分别找到此类算子最低特征值的主导渐近行为，针对$N>p^2$和$N\leq p^2$。