70 citations · 151 across the 19 of their papers we have counts for
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math.AP2013★ 1 cited
Strong competition versus fractional diffusion: the case of Lotka-Volterra interaction
Gianmaria Verzini, Alessandro Zilio
We consider a system of differential equations with nonlinear Steklov boundary conditions, related to the fractional problem $$(-Δ)^s u_i = f_i(x,u_i) - βu_i^p \sum_{j\neq i} a_{ij…
math.AP2013
Uniform Hölder regularity with small exponent in competition-fractional diffusion systems
Susanna Terracini, Gianmaria Verzini, Alessandro Zilio
For a class of competition-diffusion nonlinear systems involving fractional powers of the Laplacian, including as a special case the fractional Gross-Pitaevskii system, we prove th…
math.AP2013★ 11 cited
Entire solutions with exponential growth for an elliptic system modeling phase-separation
Nicola Soave, Alessandro Zilio
We prove the existence of entire solutions with exponential growth for the semilinear elliptic system [\begin{cases} -Δu = -u v^2 & \text{in } -Δv= -u^2 v & \text{in }…