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Cluster solutions for the Schrödinger-Poisson-Slater problem around a local minimum of the potential

- David Ruiz, Giusi Vaira
- 2011

In this paper we consider the system in R3 (0.1) { −ε2Δu + V (x)u + φ(x)u = up, −Δφ = u2, for p ∈ (1, 5). We prove the existence of multi-bump solutions whose bumps concentrate around a local minimum… (More)

- Giusi Vaira
- 2011

In this paper, we prove that the Brezis-Nirenberg problem -\Delta u = |u|^{p-1}u+\epsilon u in \Omega; u=0 on \partial \Omega where \Omega is a symmetric bounded smooth domain in R^N, N\geq 7 and p =… (More)

Let (M, g) be a compact smooth connected Riemannian manifold (without boundary) of dimension N ≥ 7. Assume M is symmetric with respect to a point ξ0 with non-vanishing Weyl’s tensor. We consider the… (More)

- Giusi Vaira
- 2015

We consider equations of the form ∆u + λV (x)e u = ρ in various two dimensional settings. We assume that V > 0 is a given function, λ > 0 is a small parameter and ρ = O(1) or ρ → +∞ as λ → 0. In a… (More)