44 research outputs found
Supercritical problems in domains with thin toroidal holes
In this paper we study the Lane-Emden-Fowler equation Here , is a smooth bounded domain in , is an
dimensional closed manifold such that
with and . We prove that,
under some symmetry assumptions, the number of sign changing solutions to
increases as goes to zero
Boundary towers of layers for some supercritical problems
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