In this article we consider the system of equations { \Delta}u_{ i}=p_{ i}(x)f_{ i}(u_{ 1},...,u_{ d}) for i=1,...,d on R^{ N}, N\geq3 and d\in{ 1,2,3,4,...}. We prove that the considered system has a bounded positive entire solution under some conditions on p_{ i} and f_{ i}. Also, we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation. Furthermore, a non-radially symmetric solution is obtained by using a lower and upper solution method.
Categories: math.AP