Study of a third‐order three‐point boundary value problem

2010 ◽  
Author(s):  
Assia Guezane‐Lakoud ◽  
Rabah Khaldi
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order

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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