Abstract
We study the following singularly perturbed Kirchhoff equation −(ϵ2a+ϵb∫R3|∇u|2dx)Δu+V(x)u=u5,u∈D1,2(R3),where ϵ>0 is a parameter, a,b>0, V∈L32(R3) is nonnegative and of critical frequency. By means of variational methods, we investigate the relation between the number of high energy semiclassical states and the topology of the zero set of V for small ϵ.
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