Existence results for a class of (p,q) Laplacian systems - Afrouzi, G. A. A.; Mirzapour, M. (Nonlinear Analysis: Modelling and Control, 2010)
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) ∈ W01,p(Ω) × W01,q(Ω).Our result depending on the local minimization.
Keywords: elliptic systems; Nehari manifold; Ekeland variational principle; local minimization