Existence of positive solutions of elliptic mixed boundary value problem

摘要

In this paper, we use variational methods to prove two existence of positive solutions of the following mixed boundary value problem: { − Δ u = f ( x , u ) , x ∈ Ω , u = 0 , x ∈ σ , ∂ u ∂ ν = g ( x , u ) , x ∈ Γ . One deals with the asymptotic behaviors of f ( x , u ) near zero and infinity and the other deals with superlinear of f ( x , u ) at infinity. MSC:35M12, 35D30.