Boundary towers of layers for some supercritical problems

Abstract

We show that in some suitable torus-like domains D some supercritical elliptic problems have an arbitrary large number of sign-changing solutions with alternate positive and negative layers which concentrate at different rates along a k-dimensional submanifold of the boundary of D as p approaches 2*_{N,K} from below.

References in corpus (3)

• Nonexistence and multiplicity of solutions to elliptic problems with supercritical exponents
• Conformal approach to cylindrical DLA
• Boundary clustered layers near the higher critical exponents

Cited by in corpus (3)

• Positive solutions to a supercritical elliptic problem which concentrate along a thin spherical hole
• Solutions to a singularly perturbed supercritical elliptic equation on a Riemannian manifold concentrating at a submanifold
• Supercritical problems in domains with thin toroidal holes