scholarly journals Several Existence Theorems of Monotone Positive Solutions for Third-Order Multipoint Boundary Value Problems

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Weihua Jiang ◽  
Fachao Li
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Existence Theorems ◽  
Boundary Value ◽  
Third Order ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems ◽  
Monotone Positive Solutions

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 On the Existence of Positive Solutions of Resonant and Nonresonant Multipoint Boundary Value Problems for Third-Order Nonlinear Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Liu Yang ◽  
Chunfang Shen ◽  
Dapeng Xie ◽  
Xiping Liu
Keyword(s):  
Positive Solutions ◽  
Existence Result ◽  
Nonlinear Differential Equations ◽  
Boundary Value ◽  
Type Theorem ◽  
Third Order ◽  
Multipoint Boundary ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Value Problems ◽  
Multipoint Boundary Value Problem

Positive solutions for a kind of third-order multipoint boundary value problem under the non-resonant conditions and the resonant conditions are considered. In the nonresonant case, by using Leggett-Williams fixed-point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using Leggett-Williams norm-type theorem due to O’Regan and Zima, existence result of at least one positive solution is established. The results obtained are valid and new for the problem discussed. Two examples are given to illustrate the main results.

scholarly journals Positive Solutions for Multipoint Boundary Value Problems for Singular Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapinar ◽  
Bessem Samet
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Coupled Fixed Point ◽  
Multipoint Boundary ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problems

A class of nonlinear multipoint boundary value problems for singular fractional differential equations is considered. By means of a coupled fixed point theorem on ordered sets, some results on the existence and uniqueness of positive solutions are obtained.

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