Large solutions for a semilinear elliptic problem with sign-changing weights

This paper focuses on an elliptic boundary blow up problem with sign-changing weights△uϵ=(a+−ϵa−)g(uϵ),x∈Ω,uϵ|∂Ω=+∞, where Ω⊂Rn(n≥1) is a bounded smooth domain and ϵ>0 is a real parameter. We verify that there exists ϵ⁎>0 such that the problem has the minimal positive large solution for any ϵ∈(0,ϵ⁎), while no positive large solutions for any ϵ>ϵ⁎. Then, by applying the local bifurcation theory, we analyze the structure of the branch produced by the positive large solutions.