scholarly journals Existence and uniqueness of monotone positive solutions for a third-order three-point boundary value problem

2018 ◽  
pp. 251-260
Author(s):  
Li Zhao ◽  
Weix an Wang ◽  
Chen bo Zhai
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Monotone Positive Solutions

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 Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
I. J. Cabrera ◽  
J. Harjani ◽  
K. B. Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Boundary Value ◽  
Point Boundary ◽  
Ordered Metric Spaces ◽  
Liouville Derivative

We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problemD0+αu(t)+f(t,u(t))=0, 0<t<1, u(0)=u′(0)=u′′(0)=0,u′′(1)=βu′′(η), where3<α≤4,D0+αis the standard Riemann-Liouville derivative andf:(0,1]×[0,∞)→[0,∞)withlim t→0+f(t,·)=∞(i.e.,fis singular att=0). Our analysis relies on a fixed point theorem in partially ordered metric spaces.

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