(untitled) (Journal of Partial Differential Equations, 2012)
We establish sufficient conditions under which the quasilinear equation -div(|∇u|^n-2∇u)+V(x)|u|^n-2u=f(x,u)|x|^β+εh(x) in R^n, has at least two nontrivial weak solutions in W^1,n (R^n) when ε > 0 is small enough, 0≤β < n, V is a continuous potential, f(x,u) behaves like expγ|u|^n/(n-1) as |u|→∞ for some γ > 0 and h≢ 0 belongs to the dual space of W^1,n (R^n).