scholarly journals Positive solutions for a nonlinear third order multipoint boundary value problem

2011 ◽  
Vol 249 (1) ◽  
pp. 177-188 ◽  
Author(s):  
Yang Liu ◽  
Zhang Weiguo ◽  
Liu Xiping ◽  
Shen Chunfang ◽  
Hua Chen
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Third Order ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problem

scholarly journals Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Liu Yang ◽  
Chunfang Shen ◽  
Dapeng Xie
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Type Theorem ◽  
Third Order ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems ◽  
First Time ◽  
Multipoint Boundary Value Problem

Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.

scholarly journals Existence of Positive Solutions for a Nonlinear Higher-Order Multipoint Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Min Zhao ◽  
Yongping Sun
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Existence Results ◽  
Monotone Iterative Method ◽  
Multipoint Boundary ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Value Problem

We study the existence of positive solutions for a nonlinear higher-order multipoint boundary value problem. By applying a monotone iterative method, some existence results of positive solutions are obtained. The main result is illustrated with an example.

scholarly journals Solvability of a Third-Order Multipoint Boundary Value Problem at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zengji Du ◽  
Bensheng Zhao ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Third Order ◽  
Multipoint Boundary ◽  
At Resonance ◽  
Problem At Resonance ◽  
Multipoint Boundary Value Problem

We discuss a third-order multipoint boundary value problem under some appropriate resonance conditions. By using the coincidence degree theory, we establish the existence result of solutions. The emphasis here is that the dimension of the linear operator is equal to two. Our results supplement other results.

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