Analytical Results on existence and stability for coupled systems of three 1st order nonlinear differential equations with nonlocal conditions using Banach contraction mapping approach

Abstract

In this work, a nonlocal-boundary value problem that includes two types of coupled systems of three first-order nonlinear differential equations with nonlocal conditions is introduced. The existence and uniqueness results
 of solutions for the Cauchy problem are obtained for certain continuous functions on time and the real line space. A local solution is obtained first, followed by a global solution whose proof employs said a contraction principle in the supremum norm. Additionally, the stability of solutions are analyzed. A local stability result is obtained first by employing continuous dependence of local solutions on the space data. In order to illustrate the link between uniform stability and global stability, in the last part of the paper we focus on a stability for global solutions. In particular, our analysis reveals that the global solutions are uniformly globally stable.