Abstract :
We mainly consider the system
⎧⎨⎩
− p(x)u = λf (x, v) in Ω,
− p(x)v = λg(x, u) in Ω,
u = v =0 on ∂Ω,
where Ω ⊂ RN is a bounded domain, p(x) is a function which satisfies some conditions, − p(x)u =
−div(|∇u|p(x)−2∇u) is called p(x)-Laplacian. We give the existence of positive solutions under some
conditions. In particular, we do not assume radial symmetric conditions on the system.
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