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

2015/06/27 by Chrouda, Mohamed Ben, Fredj, Mahmoud Ben
#31B05 and 60J45 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.08294

Abstract

The main goal is to establish necessary and sufficient conditions under which the fractional semilinear elliptic equation Δ^\fracα2 u=ρ(x) φ(u) admits nonnegative nontrivial bounded solutions in the whole space ℝ^N.

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