The main goal is to establish necessary and sufficient conditions under which the fractional semilinear elliptic equation ∆ α 2 u = ρ(x) ϕ(u) admits nonnegative nontrivial bounded solutions in the whole space R N .
For γ > 0, we are interested in blow up solutions u ∈ C + (B) of the fractional problem in the unit ball BWe distinguish particularly two orders of singularity at the boundary: solutions exploding at the same rate than δ 1− α 2 (δ denotes the Euclidean distance) and those higher singular than δ 1− α 2 . As a consequence, it will be shown that the classical Keller-Osserman condition can not be readopted in the fractional setting.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.