Existence Of Radial Solutions For Several Kinds Of Nonlinear Elliptic Systems

In this thesis,under the Keller-Osserman type condition and Osgood type condition,by using the monotone iterative method,we study the existence of entire positive radial solutions for Schr(?)dinger system containing a nonlinear operator,k-Hessian system involving a nonlinear operator and k-Hessian system with gradient term,respectively.First,we consider the Schr(?)dinger system containing a nonlinear operator under the Osgood type condition.we obtain the existence of the positive entire radial solution and the estimation of the bounded solution by applying the monotonic iterative method,and then the existence of blow-up solution and semifinite blow-up solution are obtained.Secondly,we consider the k-Hessian system involving a nonlinear operator under the Keller-Osserman type condition.By using the monotone iterative method,we obtain the existence conditions of positive radial solutions in cases of finite,infinite and semifinite.Finally,by applying the monotonic iterative method,we consider the nonlinear k-Hessian system with gradient term under the Osgood type condition.On the one hand,we obtain the existence of the positive entire radial solution and the estimation of the bounded solution in the finite case,on the other hand,the existence of blow-up solution is obtained in the infinite case.