Electron. J. Differential Equations, Vol. 2020 (2020), No. 45, pp. 1-15.

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

Qiuyue Wang, Lu Yang

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.
DOI: 10.58997/ejde.2020.45

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Qiuyue Wang
School of Mathematics and Statistics
Lanzhou University
Lanzhou 730000, China
email: wangqy17@lzu.edu.cn
Lu Yang
School of Mathematics and Statistics
Lanzhou University
Lanzhou 730000, China
email: yanglu@lzu.edu.cn

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