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

In this paper, we consider the subcritical semilinear elliptic problemequation(*λ)-Δu+u=λK(x)up+f(x)inΩ,u>0inΩ,u∈H01(Ω),where λ⩾0,N⩾3,1λ*λ>λ*. Furthermore, if there exists a positive constant K0K0 such that K(x)⩾K0K(x)⩾K0 for x∈Ωx∈Ω and ff is bounded in ΩΩ, then (*)λ(*)λ has at least one solution for λ=λ*λ=λ*.