ON A CLASS OF SINGULAR ELLIPTIC SYSTEM WITH COMBINED NONLINEAR EFFECTS

We study the existence of positive solution for the following nonlinear system −div(|x|−ap |∇u|p−2∇u) = λ |x|−(a+1)p+c1 f(u, v), x ∈ Ω, −div(|x|−bq |∇v|q−2∇v) = λ |x|−(b+1)q+c2 g(u, v), x ∈ Ω, u = v = 0, x ∈ ∂Ω, where Ω is a bounded smooth domain of RN with 0 ∈ Ω, 1 < p, q < N, 0 ≤ a < N−p p , 0 ≤ b < N−q q and c1, c2, λ are positive parameters. Here f, g : [0,∞) × [0,∞) → [0,∞) are nondecresing continuous functions and lim x→∞ f(x,A[g(x, x)] 1 q−1 ) xp−1 = 0. for every A > 0. We discuss the existence of positive solution when f and g satisfy certain additional conditions. We use the method of sub-super solutions to establish our results. 2000 Mathematics Subject Classification: 35J55, 35J65.