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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 andd\in{1,2,3,4,...}. We prove that the considered system has a bounded positiveentire solution under some conditions on p_{i} and f_{i}. Also, we give anecessary condition as well as a sufficient condition for a positive radialsolution to be large. The method of proving theorems is essentially based on asuccessive approximation. Furthermore, a non-radially symmetric solution isobtained by using a lower and upper solution method.

Radial and nonradial solutions for a semilinear elliptic system of Schr\"odinger type