4 papers
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…
Nonhomothetic complete periodic metrics with constant scalar curvature
João H. Andrade, Jeffrey S. Case, Paolo Piccione +1
We show that there are infinitely many pairwise nonhomothetic, complete, periodic metrics with constant scalar curvature that are conformal to the round metric on $S^n\setminus S^k…
Local asymptotics for singular solutions to critical Hartree equations
João Henrique Andrade, Tao Feng, Paolo Piccione +1
We investigate the qualitative properties of a critical Hartree equation defined on punctured domains. Our study has two main objectives: analyzing the asymptotic behavior near iso…
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…