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

Yaohong Li,Xiaoyan Zhang

doi:10.1155/2014/591381

Abstract

Highlights

By constructing some general type conditions and using fixed point theorem of cone, this paper investigates the existence of at least one and at least two positive solutions for systems of nonlinear higher order differential equations with integral boundary conditions
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 systems (1), let n1 = 3, n2 = 4, a1(t) = a2(t) = 1, n1(t) = n2(t) = t, f1(t, u, V) = (1+t+e−u)V1/2, and f2(t, u) = u1/2, so the assumptions (H1)–(H3) are satisfied

Summary

Introduction

By constructing some general type conditions and using fixed point theorem of cone, this paper investigates the existence of at least one and at least two positive solutions for systems of nonlinear higher order differential equations with integral boundary conditions. We consider the following systems of nonlinear mixed higher order differential equations with integral boundary conditions: u(n1) (t) + a1 (t) f1 (t, u (t) , V (t)) = 0, t ∈ (0, 1) , V(n2) (t) + a2 (t) f2 (t, u (t)) = 0, t ∈ (0, 1) , u (0) = u󸀠 (0) = ⋅ ⋅ ⋅ = u(n1−2) (0) = 0, u (1) = ∫ n1 (t) u (t) dt, (1)

Results

Conclusion