Honghui Yin,
Zuodong Yang
(2012)
Our main purpose is to establish the existence of a positive solution of the system
⎧, x ∈ Ω,
⎨, x ∈ Ω,
⎩u = v = 0, x ∈ ∂Ω,
where is a bounded domain with C² boundary, , , λ > 0 is a parameter, p(x),q(x) are functions which satisfy some conditions, and is called the p(x)-Laplacian. We give existence results and consider the asymptotic behavior of solutions near the boundary. We do not assume any symmetry conditions on the system.