Boundary towers of layers for some supercritical problems

2013/02/05 by Kim, Seunghyeok, Pistoia, Angela
#35J20 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1302.1217

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.

Related

• Positive and nodal single-layered solutions to supercritical elliptic problems above the higher critical exponents
• Bubble towers for supercritical semilinear elliptic equations
• Sign-changing blowing-up solutions for supercritical Bahri-Coron's problem
• Existence of Boundary Layers for the supercritical Lane-Emden Systems
• Positive solutions to a supercritical elliptic problem which concentrate along a thin spherical hole