A Reduction Method for Semilinear Elliptic Equations and Solutions Concentrating on Spheres
Analysis of PDEs
2014-04-02 v1
Abstract
We show that any general semilinear elliptic problem with Dirichlet or Neumann boundary conditions in an annulus A in R^2m ;m >1, invariant by the action of a certain symmetry group can be reduced to a nonhomogenous similar problem in an annulus D in R^(m+1), invariant by another related symmetry. We apply this result to prove the existence of positive and sign changing solutions of a singularly perturbed elliptic problem in A which concentrate on one or two (m-1) dimensional spheres. We also prove that the Morse indices of these solutions tend to infinity as the parameter of concentration tends to infinity.
Keywords
Cite
@article{arxiv.1210.0782,
title = {A Reduction Method for Semilinear Elliptic Equations and Solutions Concentrating on Spheres},
author = {Filomena Pacella and P. N. Srikanth},
journal= {arXiv preprint arXiv:1210.0782},
year = {2014}
}