Multi-peak solutions to Kirchhoff equations in R3 with general nonlinearity

We are concerned with the existence of multi-peak solutions to Kirchhoff equation(0.1)−(ϵ2a+ϵb∫R3|∇u|2dx)Δu+V(x)u=f(u),x∈R3, where ϵ>0 is a small parameter, a, b>0 are constants. Under general conditions of f, we construct a family positive solutions uϵ∈H1(R3) which concentrates around the isolated components of positive local minima of V as ϵ→0+. Our result generalize the previous results on single peak solutions to multi-peak solutions.