Affiliations: Department of Mathematics, Jiangxi Normal University, Nanchang, China | Departamento de Ingeniería Matemática, Universidad de Chile, Santiago, Chile. E-mail: [email protected] | Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Tours, France. E-mail: [email protected]
Abstract: Let Ω⊂RN (N≥2) be a bounded C2 domain containing 0, 0<α<1 and 0<p<N/(N−2α). If δ0 is the Dirac mass at 0 and k>0, we prove that the weakly singular solution uk of (Ek) (−Δ)αu+up=kδ0 in Ω, which vanishes in Ωc, is a classical solution of (E*) (−Δ)αu+up=0 in Ω\{0} with the same outer data. Let A=[N/2α,1+2α/N) for N=2,3 and (√5−1)/4N<α<1, otherwise, A=∅; we derive that uk converges to ∞ in whole Ω as k→∞ for p∈(0,1+2α/N)\A, while the limit of uk is a strongly singular solution of (E*) for 1+2α/N<p<N/(N−2α).
