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math.AP2023
Nodal cluster solutions for the Brezis-Nirenberg problem in dimensions
Monica Musso, Serena Rocci, Giusi Vaira
We show that the classical Brezis-Nirenberg problem $$Δu + |u|^{4 \over N-2} u + \varepsilon u = 0 ,\quad {\mbox {in}} \quad Ω, \quad u= 0 , \quad {\mbox {on}} \quad \partial Ω$$ a…
math.AP2023
Partially concentrating standing waves for weakly coupled Schrödinger systems
Benedetta Pellacci, Angela Pistoia, Giusi Vaira +1
We study the existence of standing waves for the following weakly coupled system of two Schrödinger equations in , , \[ \begin{cases} i \hslash \partial_{t}ψ_{…
math.AP2023
Positive Blow-up Solutions for a Linearly Perturbed Boundary Yamabe Problem
Sergio Cruz-Blázquez, Giusi Vaira
We consider the problem of prescribing the scalar and boundary mean curvatures via conformal deformation of the metric on a dimensional compact Riemannian manifold. We deal wi…