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

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] X C[0, 1] and applying fixed 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 K1 X K2 ⊂ C[0,1] X 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.