Positive solutions for semilinear elliptic equations with singular forcing terms

Abstract

We consider the existence of solutions to the semilinear elliptic problem(*)κ{(- Δ u + u = up + κ ∑i = 1m ci δai in  D′ (RN),; u > 0 a.e. in RN and u (x) → 0 as | x | → ∞,). with prescribed given finite points {ai}i = 1m in RN and positive numbers {ci}i = 1m, where N ≥ 3, 1 < p 0 such that (*)κ has at least two solutions if κ ∈ (0, κ*), a unique solution if κ = κ*, and no solution if κ > κ*. © 2007 Elsevier Inc. All rights reserved.