Positive Solutions for a Nonlinear Higher Order Differential System with Coupled Integral Boundary Conditions

Abstract

We investigate the existence of positive solutions for a nonlinear higher order differential system, where the differential system is coupled not only in the differential system but also through the boundary conditions. By constructing a special cone and using the fixed point theorem of cone expansion and compression of norm type, the existence of single and multiple positive solutions is established. As an application, we give some examples to demonstrate our results.

Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations

“…In recent years, there have been some significant developments in the study of ordinary differential equations and partial differential equations involving fractional derivatives with coupled boundary conditions, as shown by the papers [26,27,32,38,42,43] and the references therein. For example, by mixed monotone method, Cui et al [15] established sufficient conditions for the existence and uniqueness of positive solutions to a singular differential system with integral boundary value conditions.…”