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

• Main Authors: G. A. Afrouzi, M. Mirzapour
• Format: Article
• Language: English
• Published: Vilnius University Press 2010-10-01
• Series: Nonlinear Analysis
• Subjects: elliptic systems; Nehari manifold; Ekeland variational principle; local minimization
• Online Access: http://www.journals.vu.lt/nonlinear-analysis/article/view/14311

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.