Existence of positive solutions for nonlocal p(x)-Kirchhoff elliptic systems

Abstract

In this article, we discuss the existence of positive solutions by using sub-super solutions concepts of the following p(x)-Kirchhoff system: [EQUATION PRESENTED] where Ω ⊂ RN is a bounded smooth domain with C2 boundary ∂Ω , Δp(x)u = div (|∇u|p(x)-2∇u),p(x) ∞ C1(Ω), with 1 < p (x), is a function satisfying 1 < p-= infΩp(x) ≤ p+ = supΩp(x)