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<p<(n+2)/(n−2)(n⩾3),+ ∞ (n=2) as a typical example: − Δu+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.
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