On a boundary value problem in the half-space

In this paper, we study the existence of positive solutions and sign-changing solutions for the following boundary value problem in the half-space{Δu=0,inR+N+1,∂u∂n+λg(x)u=f(u),on∂R+N+1, where λ is a positive parameter and the nonlinear term f is superlinear at zero and asymptotically linear at infinity.