Article ID Journal Published Year Pages File Type
4622306 Journal of Mathematical Analysis and Applications 2007 13 Pages PDF
Abstract

We mainly consider the system{−Δp(x)u=λf(x,v)inΩ,−Δp(x)v=λg(x,u)inΩ,u=v=0on∂Ω, where Ω⊂RNΩ⊂RN is a bounded domain, p(x)p(x) is a function which satisfies some conditions, −Δp(x)u=−div(|∇u|p(x)−2∇u)−Δp(x)u=−div(|∇u|p(x)−2∇u) is called p(x)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.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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