Existence of multiple positive solutions of semilinear elliptic boundary value problems in the half space Original Research Article

In this paper, we prove that if QQ and ff satisfy some suitable conditions, then −Δu+u=Q(x)f(u)−Δu+u=Q(x)f(u) in View the MathML sourceR+N with the boundary condition u(y,0)=λg(y)u(y,0)=λg(y) has at least two positive solutions if 0<λ<λ∗0<λ<λ∗, a unique positive solution if λ=λ∗λ=λ∗ and no positive solution if λ>λ∗λ>λ∗.