Solutions concentrating on higher dimensional subsets for singularly perturbed elliptic equations II

We construct spike layered solutions for the semilinear elliptic equation −ε2Δu+V(x)u=K(x)up−1 on a domain which may be bounded or unbounded. The solutions concentrate simultaneously on a finite number of m-dimensional spheres in Ω. These spheres accumulate as ε→0 at a prescribed sphere in Ω whose location is determined by the potential functions V,K.