On a first-order differential system with initial and nonlocal boundary conditions

Abstract

This paper is devoted to the existence of solutions and the multiplicity of positive solutions of an initial-boundary value problem for a nonlinear first-order differential system with nonlocal conditions. The main tool is the fixed-point theorem in which we construct the novel representation of the associated Green’s functions with useful properties and define a cone in the Banach space suitably. Some examples are also given to demonstrate the validity of the main results.

Keywords

• initial-boundary value problems
• nonlinear differential system
• nonlocal conditions
• positive solutions
• the fixed-point theory
• 34b07
• 34b10
• 34b18
• 34b27