scholarly journals Monotone positive solution of nonlinear third-order two-point boundary value problem

2014 ◽  
Vol 15 (2) ◽  
pp. 743 ◽  
Author(s):  
Yongping Sun ◽  
Min Zhao ◽  
Shuihong Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Monotone Positive Solution

scholarly journals Iteration for a Third-Order Three-Point BVP with Sign-Changing Green's Function

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ya-Hong Zhao ◽  
Xing-Long Li
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solution ◽  
Green's Function ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Monotone Positive Solution

We are concerned with the following third-order three-point boundary value problem:u‴(t)=f(t,u(t)),t∈[0,1],u′(0)=u(1)=0,u″(η)+αu(0)=0, whereα∈[0,2)andη∈[2/3,1). Although corresponding Green's function is sign-changing, we still obtain the existence of monotone positive solution under some suitable conditions onfby applying iterative method. An example is also included to illustrate the main results obtained.

Positive Solution for Boundary Value Problem of Nonlinear Three-Order Difference Equation

2014 ◽  
Vol 926-930 ◽  
pp. 3665-3668
Author(s):  
Chun Li Wang ◽  
Chuan Zhi Bai ◽  
Xiao Dong Cai
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Order Difference ◽  
Order Difference Equation

In this paper we investigate the existence of positive solution of the following nonlinear discrete third-order two-point boundary value problem. whereis continuous and there existssuch that . Our approach relies on the Krasnosel'skii fixed point theorem. An example is given to demonstrate the application of the theorem obtained.

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