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math.AP2026
Delaunay solutions to the fractional Hartree equation with critical growth
João Henrique Andrade, Tao Feng, Paolo Piccione +1
We study positive solutions of the critical fractional Hartree equation with a non-removable isolated singularity at the origin. This equation is doubly nonlocal, involving both th…
math.AP2025
Asymptotic behavior of solutions to critical Hartree equations with isolated singularities
João Henrique Andrade, Tao Feng, Paolo Piccione +1
We investigate the qualitative properties of positive classical solutions to critical Hartree equations on punctured domains, assuming that as . For the…
math.AP2024
From bubbles to clusters: Multiple solutions to the Allen--Cahn system
João Henrique de Andrade, Dario Corona, Stefano Nardulli +2
We extend previous works on the multiplicity of solutions to the Allen-Cahn system on closed Riemannian manifolds by considering an arbitrary number of phases. Specifically, we sho…