Fixed: Missing prefactor in the expression of f-f*f
Fixed: 1/rho is convex, not concave.
Fixed: Miscellaneous typos and small changes to the formatting.
Added: Theorem on positivity of solutions.
Added: Reference to [CJLL20]
Added: Theorem on decay rate is now more general.
Fixed: Clarified the discussion in point 2-2 of the proof of the theorem
on decay.
Removed: open problem about positivity of solutions.
Fixed: Format of named theorems.
Fixed: Minor formatting fixes.
Fixed: In proof of decay: indenting error.
