Positive solutions of the system for nth-order singular nonlocal boundary value problems

Abstract

The paper deals with the existence and multiplicity of positive solutions to systems of nth-order singular nonlocal boundary value problems. The main tool used in the proof is fixed point index theory in cone. Some limit type conditions for ensuring the existence of positive solutions are given.

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

“…. , − 2, ( ) ( ) , (2) involving Stieltjes integrals. In particular, , are functionals of bounded variation with positive measures.…”

“…In recent years, there were many works to be done for a variety of nonlinear higher order ordinary differential system. However, most papers only focus on paying attention to the differential system with uncoupled boundary conditions (see [1][2][3][4][5] and the reference therein). Coupled boundary conditions arise in the study of reaction-diffusion equations and Sturm-Liouville problems (see [6]) and have wide applications in various fields of sciences and engineering, for example, the heat equation [7,8].…”

Boundary Value Problems for Fourth Order Nonlinearp-Laplacian Difference Equations

“…Among these approaches, the critical point theory seems to be a powerful tool to deal with this problem (see [5,[7][8][9]). However, compared to the boundary value problems of lower order difference equations ( [6,8,[10][11][12][13]), the study of boundary value problems of higher order difference equations is relatively rare (see [9,14,15]), especially the works by using the critical point theory [16]. For the background on difference equations, we refer to [17].…”

Positive Solutions for Systems of Nonlinear Higher Order Differential Equations with Integral Boundary Conditions

“…On the other hand, much effort has been devoted to the study of the existence of positive solutions for systems of nonlinear differential equations (see [13][14][15][16] and the references therein). In [13], by applying Krasnoselskii fixed point theorem in a cone, Hu and Wang obtained multiple positive solutions of boundary value problems for systems of nonlinear second-order differential equations.…”

“…In [15], by using fixed point index theory, Xie and Zhu improved the results of [14]. At the same time, boundary value problems with integral boundary conditions have received attention [16,17].…”