Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, part I

Antonio Ambrosetti, Andrea Malchiodi, Wei-Ming Ni

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143 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)427-466
Number of pages40
JournalCommunications in Mathematical Physics
Volume235
Issue number3
DOIs
StatePublished - Apr 1 2003

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