Global Journal of Pure and Applied Mathematics

We study the nonexistence of positive solutions for the system where Δ_p denotes the p-Laplacian operator defined by for p > 1 and Ω is a smooth bounded domain in R^N (N ≥ 1), ∂Ω is its smooth boundary and λ,μ are positive parameters. Let f, g: [0, ∞) → R be continuous and assume that there exist positive numbers K_i and M_i, i = 1, 2 such that f (v) ≥ K₁v^p−1 + M₁ for all v ≥ 0, and g(u) ≥ K₂u^p−1 + M₂ for all u ≥ 0. We establish the nonexistence of positive solutions when λμ is large.