Uniqueness and existence results for a third-order nonlinear multi-point boundary value problem

2008 ◽  
Vol 205 (1) ◽  
pp. 187-196 ◽  
Author(s):  
Xiaojie Lin ◽  
Zengji Du ◽  
Wenbin Liu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Existence Results ◽  
Point Boundary ◽  
Third Order ◽  
Uniqueness And Existence ◽  
Uniqueness And Existence Results

scholarly journals On the Solvability of a Resonant Third-Order Integral m-Point Boundary Value Problem on the Half-Line

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
O. F. Imaga ◽  
J. G. Oghonyon ◽  
P. O. Ogunniyi
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Results ◽  
Coincidence Degree Theory ◽  
Half Line ◽  
Point Boundary ◽  
Third Order ◽  
At Resonance

In this work, the existence of at least one solution for the following third-order integral and m -point boundary value problem on the half-line at resonance ρ t u ′ t ″ = w t , u t , u ′ t , u ″ t , t ∈ 0 , ∞ , u 0 = ∑ j = 1 m   α j ∫ 0 η j   u t d t , u ′ 0 = 0 , lim t ⟶ ∞ ρ t u ′ t ′ = 0 , will be investigated. The Mawhin’s coincidence degree theory will be used to obtain existence results while an example will be used to validate the result obatined.

scholarly journals Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Xiaojie Lin ◽  
Zhengmin Fu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Point Index ◽  
Third Order ◽  
Index Theorems ◽  
Existence Of Positive Solutions

We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problemu‴(t)+λa(t)f(u(t))=0,0<t<1,u(0)=u′(0)=0,u″(1)=∝u″(η), whereλis a positive parameter,∝∈(0,1),η∈(0,1),f:(0,∞)→(0,∞),a:(0,1)→(0,∞)are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.

scholarly journals On a Third-Order Three-Point Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
A. Guezane-Lakoud ◽  
N. Hamidane ◽  
R. Khaldi
Keyword(s):  
Boundary Value Problem ◽  
Growth Condition ◽  
Nontrivial Solution ◽  
Polynomial Growth ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Nonlinear Alternative ◽  
Generalized Polynomial ◽  
Polynomial Growth Condition

We consider a third-order three-point boundary value problem. We introduce a generalized polynomial growth condition to obtain the existence of a nontrivial solution by using Leray-Schauder nonlinear alternative, then we give an example to illustrate our results.

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