We consider the following semilinear elliptic equation on a strip: {arraylΞuβu+up=0Β inΒ RNβ1Γ(0,L),u>0,βΞ½βuβ=0Β onΒ β(RNβ1Γ(0,L))array where 1<pβ€Nβ2N+2β. When 1<p0 such that
for Lβ€Lββ, the least energy solution is trivial, i.e., doesn't depend
on xNβ, and for L>Lββ, the least energy solution is nontrivial. When Nβ₯4,p=Nβ2N+2β, it is shown that there are two numbers
Lββ<Lβββ such that the least energy solution is trivial when Lβ€Lββ, the least energy solution is nontrivial when Lβ(Lββ,Lβββ],
and the least energy solution does not exist when L>Lβββ. A connection
with Delaunay surfaces in CMC theory is also made.Comment: typos corrected and uniqueness adde