We deal with the existence of positive radial solutions concentrating on spheres to a class of singularly perturbed elliptic problems like −ε2u + V (|x|)u = up, u ∈ H1(Rn). Under suitable assumptions on the auxiliary potential M(r) = rn−1V θ (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.

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

Ambrosetti, Antonio
;
Malchiodi, Andrea;
2003

Abstract

We deal with the existence of positive radial solutions concentrating on spheres to a class of singularly perturbed elliptic problems like −ε2u + V (|x|)u = up, u ∈ H1(Rn). Under suitable assumptions on the auxiliary potential M(r) = rn−1V θ (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.
2003
Settore MAT/05 - Analisi Matematica
   Variational Methods and Nonlinear Differential Equations.
   M.U.R.S.T.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/56046
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