Existence of multiple positive solutions of subcritical semilinear elliptic problems in exterior strip domains

In this paper, we consider the subcritical semilinear elliptic problem-Δu+u=λK(x)up+f(x)inΩ,u>0inΩ, u∈H01(Ω),where λ≥0,N≥3,1<p<(N+2)/(N-2), and Ω is an exterior strip domain in RN. Under some suitable conditions on K and f, we show that there exists a positive constant λ*, λ* depending on K and f, such that (*)λ has exactly two solutions if λ∈(0,λ*) and no solution if λ>λ*. Furthermore, if there exists a positive constant K0 such that K(x)≥K0 for x∈Ω and f is bounded in Ω, then (*)λ has at least one solution for λ=λ*.