Necessary and sufficient conditions of existence for a system involving the p-Laplacian (1

In this work, we study the existence of positive solutions for the system where Δpu=div( up−2 u) is the p-Laplacian (1μ*. In some case we can have μ*=μ* because these parameters depend on p,N and the growth of f and g. The existence result is related to a sub,super-solution methods and the nonexistence result is a consequence of Piconeʹs identity.