Overdetermined elliptic problems in onduloid-type domains with general nonlinearities

In this paper, we prove the existence of nontrivial unbounded domains Ω⊂Rn+1,n≥1, bifurcating from straight cylinder B×R (where B is unit ball Rn), such that overdetermined elliptic problem{Δu+f(u)=0in Ω, u=0on ∂Ω, ∂νu=constanton has a positive bounded solution. We will result for very general class functions f:[0,+∞)→R. Roughly speaking, only ask Dirichlet problem in admits nondegenerate The proof uses local bifurcation argument.