On Positive Solutions For Nonlinear Fourth-order Systems Of Ordinary Differential Equations

This paper is concerned with the existence of positive solutions for nonlinear fourth-order systems of ordinary differential equations in which one system is coupled by a second-order equation and a fourth-order equation and the other consists of two fourth-order equations.By virtue of the least eigenvalue of linear eigenvalue problems for a second-order equation and a fourth-order equation,we present some sufficient conditions to guarantee the existence of positive solutions for the above two systems,which is proved by the fixed point index theory.