SOME REMARK ON THE NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME a, P-LAPLACIAN SYSTEMS

Abstract. This paper deals with nonexistence result for positive solution in C 1 (Ω) to the following reaction-diffusion system −△a,pu = a1v p−1 − b1v γ−1 − c, x ∈ Ω, −△a,pv = a1u p−1 − b1u γ−1 − c, x ∈ Ω, u = 0 = v, x ∈ ∂Ω, (0.1) where △a,p denotes the a, p-Laplacian operator defined by △a,pz = div(a | ∇z | p−2 ∇z); p> 1, γ(> p); a1, b1 and c are positive constant, Ω is a smooth bounded domain in R N (N ≥ 1) with smooth boundary and a(x) ∈ L ∞ (Ω), a(x) ≥ a0> 0 for all x ∈ Ω. 1. Introduction an