EUDML

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Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem

Angela Pistoia; Tobias Weth — 2007

Annales de l'I.H.P. Analyse non linéaire

Existence, multiplicity and profile of sign-changing clustered solutions of a semiclassical nonlinear Schrödinger equation

Teresa D'Aprile; Angela Pistoia — 2009

Annales de l'I.H.P. Analyse non linéaire

Persistence of Coron’s solution in nearly critical problems

Monica Musso; Angela Pistoia — 2007

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider the problem $\{\begin{matrix} - Δ u = u^{\frac{N + 2}{N - 2} + λ} & in Ω ∖ ε ω, \\ u > 0 & in Ω ∖ ε ω, \\ u = 0 & on \partial (Ω ∖ ε ω), \end{matrix}$ where $Ω$ and $ω$ are smooth bounded domains in $ℝ^{N}$ , $N \geq 3$ , $ε > 0$ and $λ \in ℝ .$ We prove that if the size of the hole $ε$ goes to zero and if, simultaneously, the parameter $λ$ goes to zero at the appropriate rate, then the problem has a solution which blows up at the origin.