Non-existence of positive solutions of Lane-Emden systems

In this paper we consider (component-wise) positive solutions of the weakly coupled systemwhere p, q > 0 and n 3 is the dimension of the space, and are concerned with the question of non-existence of such solutions.This system arises in chemical, biological and physical studies, and has been investigated by several authors, see for example [3,8,9] and references therein.The system (I) is a natural extension of the celebrated Lane-Emden equation, and we thus refer to it as the Lane-Emden system.The Lane-Emden equation