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Article Dans Une Revue Calculus of Variations and Partial Differential Equations Année : 1995

On a variational problem with lack of compactness: the topological effect of the critical points at infinity

Résumé

We study the subcritical problems (P_ɛ) : −Δu = u^(p−ɛ), u>0 on Ω, u=0 on ∂Ω, Ω being a smooth and bounded domain in ℝ^N, N≥3, p+1=2N/N−2 the critical Sobolev exponent and ɛ>0 going to zero — in order to compute the difference of topology that the critical points at infinity induce between the level sets of the functional corresponding to the limit case (P_0).
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Dates et versions

hal-00943456 , version 1 (22-12-2016)

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  • HAL Id : hal-00943456 , version 1

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Abbas Bahri, Yanyan Li, Olivier Rey. On a variational problem with lack of compactness: the topological effect of the critical points at infinity. Calculus of Variations and Partial Differential Equations, 1995, 3, pp.67-94. ⟨hal-00943456⟩
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