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

We mainly consider the existence and asymptotic behavior of positive solutions of the following system View the MathML source{−△p(x)u=λp(x)f(v)inΩ,−△p(x)v=λp(x)g(u)inΩ,u=v=0on∂Ω, Turn MathJax on where Ω⊂RNΩ⊂RN is a bounded domain with C2C2 boundary ∂Ω∂Ω, View the MathML source10,where p−=infx∈Ωp(x). Turn MathJax on 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).