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Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent
Jean Van Schaftingen, Jiankang Xia
We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation \[ -Δu+ u=\big(I_α*|u|^{\fracα{N}+1}\big)|…
Groundstates of the Choquard equations with a sign-changing self-interaction potential
Luca Battaglia, Jean Van Schaftingen
We consider a nonlinear Choquard equation when the self-interaction potential is unbounded from below. Under…
Groundstates for Choquard type equations with Hardy-Littlewood-Sobolev lower critical exponent
Daniele Cassani, Jean Van Schaftingen, Jianjun Zhang
For the Choquard equation, which is a nonlocal nonlinear Schrödinger type equation, , in where $N\g…
Sobolev mappings: from liquid crystals to irrigation via degree theory
Jean Van Schaftingen
Sobolev spaces are a natural framework for the analysis of problems in partial differential equations and calculus of variations. Some physical and geometric contexts, such as liqu…