Existence of Large Solutions for Quasilinear Elliptic Equation

Abstract. In this paper, we consider the problem(−div(|∇u|p−2∇u) = λu − b(x)h(u), x ∈ Ω u=+∞, on ∂Ω. where Ω is a smooth bounded domain in RN. The weight function b(x) is a non-negative continuous function in the domain, h(u) is locally Lipschitz continuous, h(u)/up−1 is increasing on (0,∞) and h(u) ∼ Hum(p−1) for sufficiently large u with H> 0 and m> 1. We establish conditions sufficient to ensure the existence of positive large solutions of the equation. 1