Nonradial blow-up solutions of sublinear elliptic equations with gradient term

Original · EN

Let f be a continuous and non-decreasing function such that f>0 on (0,∞), f(0)=0, _s≥ 1f(s)/s< ∞ and let p be a non-negative continuous function. We study the existence and nonexistence of explosive solutions to the equation Δu+|∇ u|=p(x)f(u) in Ω, where Ω is either a smooth bounded domain or Ω=ⁿ. If Ω is bounded we prove that the above problem has never a blow-up boundary solution. Since f does not satisfy the Keller-Osserman growth condition at infinity, we supply in the case Ω=ⁿ a necessary and sufficient condition for the existence of a positive solution that blows up at infinity.