On positive weak solutions for a class of quasilinear elliptic systems

In this paper, we study the existence and nonexistence of positive weak solution for the quasilinear elliptic system -Δpu=λuαvγ,-Δqv=λuδvβ with zero Dirichlet boundary condition in bounded domain Ω⊂RN. A critical exponent is obtained for existence and nonexistence of positive weak solution.