Existence and Nonexistence of Positive Solutions for a System of Higher-Order Di erential Equations with Integral Boundary Conditions

Abstract

In this paper, we investigate the existence and nonexistence of positive solutions for a system of nonlinear higher-order ordinary differential equations with Riemann-Stieltjes integral boundary conditions which contain some positive constants.

Existence of nontrivial solutions for higher order ordinary differential equations

“…In recent years, the existence, multiplicity and nonexistence of positive solutions for higher order differential equations have been extensively studied using different methods, such as, fixed point methods in cones, method of upper and lower solutions, nonlinear alternatives of Leray-Schauder and variational methods. We refer the readers to [1,2,3,4,5,6,7,8] and the references therein. To the best of our knowledge, using fixed point theorems and the method of upper and lower solutions, the existence, multiplicity and nonexistence results of positive solutions for the nonlinear differential systems with eigenvalue parameters were established in [9,10]…”