On a new Kato class and positive solutions of Dirichlet problems for the fractional Laplacian in bounded domains

Existence and nonexistence of positive solutions to the fractional equation Δ^α/2 u = –u^γ in bounded domains

“…The following important result is due to [12,Proposition 7] and provides some useful estimates of the potential…”

Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains

“…Proposition 9 (see [26,Corollary 6]). Let be a nonnegative function in ( ); then the family of functions…”

“…For more examples of functions belonging to ( ), we refer to [26]. Note that for the classical case (i.e., = 2) the class 2 ( ) was introduced and studied in [27].…”

Nonnegative Entire Bounded Solutions to some Semilinear Equations Involving the Fractional Laplacian

“…Recently, several studies have been performed for classical elliptic equations with the Laplacian operator substituted by its fractional powers [2,4,8,16,18,[31][32][33]44] by using almostly variational and partial differential equations's related techniques. In particular, there has been an interest to the solutions in the whole space R N (see, for instance, [2,8,32]).…”