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

Abstract

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) ∈ W01,p(Ω) × W01,q(Ω). Our result depending on the local minimization.

Keywords

• elliptic systems
• Nehari manifold
• Ekeland variational principle
• local minimization