A Laplacian System With Sign-Changing Weight Function

We prove the existence of at least one positive solution for the Laplacian system\ -Δv=λa(x)|v|^{q-2}v+β\fracβ{α+β}b(x)|u|^α|v|^{β-2}v&$for$x\inΩ$$ \end{array}\right. On a bounded region $\mathrm{\Omega }$ by using the Nehari manifold and the fibering maps associated with the Euler functional for the system.