Existence Of Positive Solutions For Elliptic Systems

In this paper,we are concerned with the existence of positive solutions for the sev-eral elliptic equations.Firstly,we consider a class of p-Laplace systems and get the existence of positive solution for this system by use of sub-supersolution method and Leray-Schauder degree theory.Secondly,we discuss the existence of the positive solu-tion for the Laplace equation(system)and the p-Laplace equation with the Logistic type nonlinear terms.Finally,applying the product formula of the fixed point index and the fixed point index theory in cones,we establish the existence of positive solutions for the"super-sublinear" and "sub-sublinear" elliptic systems of second order with weight functions.