Monica Musso

Sign Changing Tower of Bubbles for an Elliptic Problem at the Critical Exponent in Pierced Non-Symmetric Domains

We consider the problem in Ωϵ, u = 0 on ∂Ωϵ, where Ωϵ: = Ω \ {B(a, ϵ) ∪ B(b, ϵ)}, with Ω a bounded smooth domain in ℝ N , N ≥ 3, a ≠ b two points in Ω, and ϵ is a positive small parameter. As ϵ goes to zero, we construct sign changing solutions with multiple blow up both at a and at b.

Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation

We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrodinger type equations ?u-u+f(u)=0 in R N , u?H 1 (R N ) , where N=2 . Under natural conditions on the nonlinearity f , we prove the existence of infinitely many nonradial solutions in any dimension N=2 . Our result complements earlier works of Bartsch and Willem (N=4 or N=6 ) and Lorca-Ubilla (N=5 ) where solutions invariant under the action of O(2)×O(N-2) are constructed. In contrast, the solutions we construct are invariant under the action of D k ×O(N-2) where D k ?O(2) denotes the dihedral group of rotations and reflexions leaving a regular planar polygon with k sides invariant, for some integer k=7 , but they are not invariant under the action of O(2)×O(N-2) .

The Supercritical Lane-Emden-Fowler Equation in Exterior Domains

We consider the exterior problem where 𝒟 is a bounded, smooth domain in ℝ N , for supercritical powers p > 1. We prove that if N ≥ 4 and , then this problem admits infinitely many solutions. If 𝒟 is symmetric with respect to N axes, this result holds whenever N ≥ 3 and .

Singular limits for the bi-Laplacian operator with exponential nonlinearity in R4

Let

Nondegeneracy of entire solutions of a singular Liouvillle equation

\Omega

Two-dimensional Euler flows with concentrated vorticities

be a bounded smooth domain in

A Morse index theorem for perturbed geodesics on semi-Riemannian manifolds

\mathbb{R}^{4}

Bubbling on boundary submanifolds for the Lin–Ni–Takagi problem at higher critical exponents

such that for some integer

Double blow-up solutions for aBrezis-Nirenberg type problem}

d\geq1

Triple Junction Solutions for a Singularly Perturbed Neumann Problem

its