Nonnegative entire bounded solutions to some semilinear equations involving the fractional Laplacian

Blow up boundary solutions of some semilinear fractional equations in the unit ball

“…In the following proposition, we would like to prove the existence of a solution u ∈ C + (D) to the same problem but dropping the boundedness of the boundary datum f, thus extending the result in [5].…”

“…holds for every nonnegative function ϕ belonging to the space C ∞ c (U ). We first quote from [5] the following lemma which states a straightforward and useful fact.…”

“…It should be noticed that the comparison principle as stated in the above lemma become more or less a classical result and it is widely used in the literature ( [5,14]...). Also, as we alluded to before, the minimum principle and comparison results require information on the solutions in the whole complement of the domain and not only at the boundary, consistently with the nonlocal character of the operator ∆…”