From the text: The authors study the system of coupled elliptic equations: \[ \Delta w-\beta w+w v=0,\qquad \Delta v-\alpha v+w^2/2=0 \] in a smooth bounded region \(\Omega\subset\mathbb R^n\) with Dirichlet homogeneous boundary conditions. Then they show that solutions are critical points of the functional \(I\colon H^1_0(\Omega)\times H^1_0(\Omega)\to\mathbb R\) given by \[ I(w,v)={1\over2}\int_\Omega (|\nabla w|^2+|\nabla v|^2+\beta w^2 +\alpha v^2 -vw^2), \] if \(\alpha,\beta\) are larger than \(-\lambda_1\), the first eigenvalue of the system of Laplacians. They also show that there exists a critical point by the mountain pass theorem.