Global stability of traveling waves for delay reaction-diffusion systems without quasi-monotonicity

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. For more information see https://ejde.math.txstate.edu/Volumes/2020/45/abstr.html