On the solvability of nonlinear first-order boundary-value problems

Abstract

This article investigates the existence of solutions to first-order nonlinear boundary-value problems (BVPs) involving systems of ordinary differential equations and two-point boundary conditions. Some sufficient conditions are presented that will ensure solvability. The main tools employed are novel differential inequalities and fixed-point methods.

Keywords

• Existence of solutions
• boundary value problems
• differential equations
• fixed-point methods
• differential inequalities.