Existence of positive solutions for some nonlinear elliptic equations on unbounded domains with cylindrical ends

Abstract In this paper, we study the existence of positive solutions to nonlinear elliptic boundary value problems on unbounded domains ω⊂ R n with cylindrical ends for a general nonlinear term f ( u ) including f(u)=u p + ,1 ∞ (n=2) as a typical example: − Δ u+λu=f(u),u>0 (x∈ω), u| ∂ω =0, u(x)→0 (|x|→∞) by using the mountain pass approach. The geometry of ω plays an important role in our analysis.