Large Solution of Quasilinear Elliptic Equations under the Keller-Osserman Condition
G. A. Afrouzi, Saeid Shokooh · 2010
In this paper, our main purpose is to consider the quasilinear equation div(|∇u| p−2 ∇u )= a(x)f (u) on a domain Ω ⊆ R N ,N ≥ 3, where a is a nonnegative nontrivial continuous function and f is continuous and nondecreasing on [0, ∞], satisfies f (0) = 0,f(s) > 0 for s> 0 and the Keller-Osserman condition ∞ 1 (F (s)) −1/p ds = ∞ where F (s )= s 0 f (t)dt. We establish condition on the function a that are necessary and sufficient for the existence of positive solutions, bounded and unbounded, of the given equation. Mathematics Subject Classification: 35J60, 35B30, 35B40