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Article Dans Une Revue Communications in Contemporary Mathematics Année : 2003

A nonexistence result of single peaked solutions to a supercritical nonlinear problem

Résumé

This paper is concerned with the nonlinear elliptic problem (Pε): -Δu = up+ε, u > 0 in Ω; u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 3, p + 1 = 2n/(n - 2) is the critical Sobolev exponent and ε is a small positive parameter. In contrast with the subcritical problem (P- ε) studied by Han [11] and Rey [17], we show that (Pε) has no single peaked solution for small ε.
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Dates et versions

hal-00943506 , version 1 (07-02-2014)

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Mohamed Ben Ayed, Khalil El Mehdi, Massimo Grossi, Olivier Rey. A nonexistence result of single peaked solutions to a supercritical nonlinear problem. Communications in Contemporary Mathematics, 2003, 5 (2), pp.179-195. ⟨10.1142/S0219199703000951⟩. ⟨hal-00943506⟩
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