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

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yaohong Li ◽  
Haiyan Zhang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Higher Order ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression

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.

scholarly journals Positive Solutions for(n-1,1)-Type Singular Fractional Differential System with Coupled Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ying Wang ◽  
Lishan Liu ◽  
Xinguang Zhang ◽  
Yonghong Wu
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Coupled Integral Boundary Conditions ◽  
Existence Of Positive Solutions ◽  
Singular Fractional Differential System ◽  
Fractional Differential

We study the positive solutions of the(n-1,1)-type fractional differential system with coupled integral boundary conditions. The conditions for the existence of positive solutions to the system are established. In addition, we derive explicit formulae for the estimation of the positive solutions and obtain the unique positive solution when certain additional conditions hold. An example is then given to demonstrate the validity of our main results.

scholarly journals Positive solutions of nth-order impulsive differential equations with integral boundary conditions

2016 ◽  
Vol 24 (1) ◽  
pp. 243-261
Author(s):  
Fatma Tokmak Fen ◽  
Ilkay Yaslan Karaca
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Impulsive Differential Equations ◽  
Integral Boundary ◽  
Impulsive Boundary Value Problem ◽  
Existence And Nonexistence ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression

AbstractThis paper is concerned with the existence and nonexistence of positive solutions of nth-order impulsive boundary value problem with integral boundary conditions. The fixed point theorem of cone expansion and compression is used to investigate the existence of at least one positive solution. Also, an example is given to illustrate the effective of our results.

Sign in / Sign up

Export Citation Format

Share Document