4 papers · 1 filter
Qualitative analysis of energy ground states for magnetic focusing Gross-Pitaevskii equations
Xiaoming An, Lun Guo, Xiao Luo +1
We prove the uniqueness, asymptotics, symmetry, and orbital stability of energy ground states for 3D magnetic Gross-Pitaevskii equations under mild conditions on the electric poten…
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…
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…
Infinitely many solutions for elliptic equations with non-symmetric nonlinearities
Riccardo Molle, Donato Passaeo
We deal with the existence of infinitely many solutions for a class of elliptic problems with non-symmetric nonlinearities. Our result, which is motivated by a well known conjectur…