Existence of multiple positive solutions of semilinear elliptic equations in esteban-lions domains with holes

In this article, we consider the semilinear elliptic equation, where λ ≥ 0, N ≥ 2, 1 < p < 2* - 1 and Ω is the upper semi-strip domain with a hole in R^N. Under some suitable conditions on K and h, we show that there exists a positive constant λ* such that equation (*)_λ has at least two solutions if λ ∈ (0, λ*), a unique solution if λ = 0 or λ = λ* and no solution if λ > λ*. We also establish the asymptotic behavior and some further properties of positive solutions of equation (*)_λ.