Benedetta Noris

Increasing radial solutions for Neumann problems without growth restrictions

Abstract We study the existence of positive increasing radial solutions for superlinear Neumann problems in the ball. We do not impose any growth condition on the nonlinearity at infinity and our assumptions allow for interactions with the spectrum. In our approach we use both topological and variational arguments, and we overcome the lack of compactness by considering the cone of nonnegative, nondecreasing radial functions of H 1 ( B ) .

Positive constrained minimizers for supercritical problems in the ball

We provide a sufficient condition for the existence of a positive solution to −∆u + V (|x|)u = u in B1, when p is large enough. Here B1 is the unit ball of R , n ≥ 2, and we deal both with Neumann and Dirichlet homogeneous boundary conditions. The solution turns to be a constrained minimum of the associated energy functional. As an application we show that, in case V (|x|) ≥ 0, V 6≡ 0 is smooth and p is sufficiently large, the Neumann problem always admits a solution.

Thomas–Fermi Approximation for Coexisting Two Component Bose–Einstein Condensates and Nonexistence of Vortices for Small Rotation

We study minimizers of a Gross–Pitaevskii energy describing a two- component Bose–Einstein condensate confined in a radially symmetric harmonic trap and set into rotation. We consider the case of coexistence of the components in the Thomas–Fermi regime, where a small parameter

Uniform Hölder Bounds for Nonlinear Schrödinger Systems with Strong Competition

{\varepsilon}

Uniform H\"older bounds for nonlinear Schr\"odinger systems with strong competition

ε conveys a singular perturbation. The minimizer of the energy without rotation is determined as the positive solution of a system of coupled PDEs, for which we show uniqueness. The limiting problem for

Nodal sets of magnetic Schroedinger operators of Aharonov-Bohm type and energy minimizing partitions

{\varepsilon =0}