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

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 $N\le p^2$.

19 pages