Solution-tube and existence results for fourth-order differential equations system

Abstract

In the present paper, we examine the existence of solutions to fourth-order differential equation systems when the $ L^{1} $-Carathéodory function is on the right-hand side. A concept of solution-tube for these issues is presented. The concepts of upper and lower solutions for fourth-order differential equations are extended to systems owing to this idea.

Keywords

• fourth-order systems of differential equations
• iterative methods
• solution-tubes
• existence theorems
• leray-schauder degree