Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 45, pp. 1-15.

Title: Positive solutions for a nonlinear system of fourth-order ordinary 
       differential equations
       
Authors: Qiuyue Wang (Lanzhou Univ., Lanzhou, China)
         Lu Yang     (Lanzhou Univ., Lanzhou, China)

Abstract:
 In this article, we consider the existence of positive solutions for a nonlinear
 system of fourth-order ordinary differential equations. By constructing a single
 cone $P$ in the product space $C[0, 1] \times C[0, 1]$ and applying fixed point
 theorem in cones, we establish the existence of positive solutions for a system
 in which the nonlinear terms are both superlinear or sublinear.
 In addition, by the construction of the product cone 
$K_1 \times K_2 \subset C[0, 1] \times C[0, 1]$ along with the product formula of fixed point
 theory on a product cone, we investigate the  existence of positive solutions
 involving nonlinear terms, one uniformly superlinear or sublinear, and the other
 locally uniformly  sublinear or superlinear.
 
Submitted December 9, 2019. Published May 19, 2020.
Math Subject Classifications: 34B18, 47H11, 47N20.
Key Words: Positive solution; fixed point theory; ordinary differential equation.