Existence results for a class of (p,q) Laplacian systems

Abstract

We establish the existence of a nontrivial solution for inhomogeneous quasilinear elliptic systems:
−∆_pu = λ a(x) u |u|^γ−2 + α (α + β)^–1 b(x) u |u|^α−2 |v|^β + f    in Ω,
−∆_qv = µ d(x) v |v|^γ−2 + β (α + β)^–1 b(x) |u|^α v |v|^β−2 + g    in Ω,
(u,v) ∈ W₀^1,p(Ω) × W₀^1,q(Ω).
Our result depending on the local minimization.