Existence and asymptotic behavior of positive solutions for variable exponent elliptic systems

We mainly consider the existence and asymptotic behavior of positive solutions of the following system {−△p(x)u=λp(x)f(v)inΩ,−△p(x)v=λp(x)g(u)inΩ,u=v=0on∂Ω, where Ω⊂RNΩ⊂RN is a bounded domain with C2C2 boundary ∂Ω∂Ω, 10,where p−=infx∈Ωp(x).In particular, we do not assume any symmetric condition, and we do not assume any sign condition on f(0)f(0) and g(0)g(0).