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math.AP2023
Positive solutions to nonlinear elliptic problems involving Sobolev exponent
Carlo Mercuri, Riccardo Molle
In this paper we consider nonlinear elliptic PDEs of the type $$-Δ_p u+a(x)|u|^{p-2}u=|u|^{p^*-2}u \qquad \mbox{ in }Ω,$$ where and is the critical Sobolev e…
math.AP2023
Normalised solutions and limit profiles of the defocusing Gross-Pitaevskii-Poisson equation
Riccardo Molle, Vitaly Moroz, Giuseppe Riey
We study normalised solutions of the stationary Gross-Pitaevskii-Poisson (GPP) equation with a defocusing local nonlinear term, $$-Δu+λu+|u|^2u =(I_α*|u|^2)u\quad\text{in $\mathbb…