TY - JOUR
T1 - Singularly perturbed elliptic equations with symmetry
T2 - Existence of solutions concentrating on spheres, part I
AU - Ambrosetti, Antonio
AU - Malchiodi, Andrea
AU - Ni, Wei Ming
PY - 2003/4
Y1 - 2003/4
N2 - We deal with the existence of positive radial solutions concentrating on spheres to a class of singularly perturbed elliptic problems like -ε2 Δu + V(|x|)u = up, u ∈ H1 (ℝn). Under suitable assumptions on the auxiliary potential M(r) = rn-1 Vθ(r), θ(p + 1)/(p - 1) - 1/2, we provide necessary and sufficient conditions for concentration as well as the bifurcation of non-radial solutions.
AB - We deal with the existence of positive radial solutions concentrating on spheres to a class of singularly perturbed elliptic problems like -ε2 Δu + V(|x|)u = up, u ∈ H1 (ℝn). Under suitable assumptions on the auxiliary potential M(r) = rn-1 Vθ(r), θ(p + 1)/(p - 1) - 1/2, we provide necessary and sufficient conditions for concentration as well as the bifurcation of non-radial solutions.
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U2 - 10.1007/s00220-003-0811-y
DO - 10.1007/s00220-003-0811-y
M3 - Article
AN - SCOPUS:0038609648
SN - 0010-3616
VL - 235
SP - 427
EP - 466
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 3
ER -