Existence of global positive solutions of semilinear elliptic equations

Abstract

Using a very simple approach, we prove the existence of asymptotically vanishing global positive solutions of the semilinear elliptic equation Δ u + f ( x , u ) + g ( | x | ) x ⋅ ∇ u = 0 in all of R n , n ≥ 3 . In particular, earlier conditions on the negative part of the function f are dropped.