TY - JOUR
T1 - Singularly perturbed elliptic equations with symmetry
T2 - Existence of solutions concentrating on spheres, part II
AU - Ambrosetti, Antonio
AU - Malchiodi, Andrea
AU - Ni, Wei Ming
PY - 2004
Y1 - 2004
N2 - We study the equation -ε2Δu + V(|x|)u = u p, with ε > 0 and p > 1, in balls or annuli of ℝn, under Neumann or Dirichlet boundary conditions. As ε tends to zero we prove existence of radial solutions, with the profile of an interior one-dimensional spike, concentrated near some sphere. Of particular interest are the different, or opposite, effects created by the Neumann or Dirichlet boundary conditions on the existence as well as the locations of the concentration sets of solutions.
AB - We study the equation -ε2Δu + V(|x|)u = u p, with ε > 0 and p > 1, in balls or annuli of ℝn, under Neumann or Dirichlet boundary conditions. As ε tends to zero we prove existence of radial solutions, with the profile of an interior one-dimensional spike, concentrated near some sphere. Of particular interest are the different, or opposite, effects created by the Neumann or Dirichlet boundary conditions on the existence as well as the locations of the concentration sets of solutions.
KW - Local inversion
KW - Singularly perturbed elliptic problems
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U2 - 10.1512/iumj.2004.53.2400
DO - 10.1512/iumj.2004.53.2400
M3 - Article
AN - SCOPUS:3042688938
SN - 0022-2518
VL - 53
SP - 297
EP - 329
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
IS - 2
ER -