Positive solutions for a nonlinear system of fourth-order ordinary differential equations

• Main Authors: Qiuyue Wang, Lu Yang
• Format: Article
• Language: English
• Published: Texas State University 2020-05-01
• Series: Electronic Journal of Differential Equations
• Subjects: positive solution; fixed point theory; ordinary differential equation
• Online Access: http://ejde.math.txstate.edu/Volumes/2020/45/abstr.html

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.