scholarly journals Positive Solutions for a Fractional Boundary Value Problem with a Perturbation Term

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Yumei Zou
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Perturbation Term ◽  
Existence Of Positive Solutions

We obtain some new upper and lower estimates for the Green’s function associated with a fractional boundary value problem with a perturbation term. Criteria for the existence of positive solutions of the problem are then obtained based on it.

scholarly journals Existence of Positive Solutions for Nonlinear Third-Order Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Tiaoxia Dun ◽  
Pengyu Chen
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Boundary Value ◽  
Index Theorem ◽  
Third Order ◽  
Existence Of Positive Solutions ◽  
Fixed Point Index Theorem ◽  
Linear Boundary Value Problem

We are concerned with the existence of positive solutions for the nonlinear third-order three-point boundary value problemu′′′(t)+λg(t)f(u(t))=0,0<t<1,u(0)=αu(η),u′(0)=u′′(1)=0, where0<η<1,0<α<1,λis a positive parameter,g:(0,1)→[0,∞),  and  f:[0,∞)→[0,∞)is continuous. We construct Green’s function for the associated linear boundary value problem and obtain some useful properties of Green’s function. Finally, by using fixed-point index theorem in cones, we establish the existence results of positive solutions for the boundary value problem an example illustrates the application of the results obtained.

scholarly journals Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongjie Liu ◽  
Xiao Fu ◽  
Liangping Qi
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

scholarly journals Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqing Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.

scholarly journals A New Proof for Lyapunov-Type Inequality on the Fractional Boundary Value Problem

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 29
Author(s):  
Yumei Zou ◽  
Xin Zhang ◽  
Hongyu Li
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Boundary Value ◽  
Type Inequality ◽  
Fractional Boundary Value Problem ◽  
Lyapunov Type Inequality ◽  
Fractional Boundary Value Problems

In this article, some new Lyapunov-type inequalities for a class of fractional boundary value problems are established by use of the nonsymmetry property of Green’s function corresponding to appropriate boundary conditions.

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