Concentration of solutions to elliptic equations with critical nonlinearity

Olivier Rey (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We study the asymptotic behavior as ε goes to zero of solutions in H^1_0(Ω ) to the equation: -Δu = u∣u∣^4/(N-2) + εf(x), where Ω is a bounded domain in ℝ^N, N≥3. Wh show the existence of solutions to the problem which blow up at some well defined points, depending on f, for ε = 0.

Domaines: Equations aux dérivées partielles [math.AP]

Olivier Rey. Concentration of solutions to elliptic equations with critical nonlinearity. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1992, 9 (2), pp.201-218. ⟨hal-00943450⟩