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 Blow-Up Solutions for a Singular Nonlinear Hadamard Fractional Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Imed Bachar ◽  
Said Mesloub
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Blow Up ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Fractional Boundary Value Problems

We consider singular nonlinear Hadamard fractional boundary value problems. Using properties of Green’s function and a fixed point theorem, we show that the problem has positive solutions which blow up. Finally, some examples are provided to explain the applications of the 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 Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Moustafa El-Shahed
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Nonexistence ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem:D0+αu(t)+λa(t) f(u(t))=0, 0<t<1, u(0)=u′(0)=u′(1)=0,where2<α<3is a real number andD0+αis the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.

Existence of positive solutions for second-order undamped Sturm–Liouville boundary value problems

2016 ◽  
Vol 09 (04) ◽  
pp. 1650089 ◽  
Author(s):  
K. R. Prasad ◽  
L. T. Wesen ◽  
N. Sreedhar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

In this paper, we consider the second-order differential equations of the form [Formula: see text] satisfying the Sturm–Liouville boundary conditions [Formula: see text] where [Formula: see text]. By an application of Avery–Henderson fixed point theorem, we establish conditions for the existence of multiple positive solutions to the boundary value problem.

scholarly journals Positive solutions of impulsive time-scale boundary value problems with p-Laplacian on the half-line

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 415-433
Author(s):  
Karaca Yaslan ◽  
Aycan Sinanoglu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scale ◽  
Boundary Value ◽  
Dynamic Equations ◽  
Half Line ◽  
Existence Of Positive Solutions

In this paper, four functionals fixed point theorem is used to investigate the existence of positive solutions for second-order time-scale boundary value problem of impulsive dynamic equations on the half-line.

scholarly journals Positive Solutions for Boundary Value Problem of Nonlinear Fractional -Difference Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Moustafa El-Shahed ◽  
Farah M. Al-Askar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Fractional Difference ◽  
Fractional Difference Equation

We investigate the existence of multiple positive solutions to the nonlinear -fractional boundary value problem , , by using a fixed point theorem in a cone.

scholarly journals Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
A. Guezane-Lakoud ◽  
R. Khaldi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Integral ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Deviating Argument

This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.

Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem

2017 ◽  
Vol 67 (2) ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak Fen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Impulsive Boundary Value Problem

AbstractIn this paper, six functionals fixed point theorem is used to investigate the existence of at least three positive solutions for a nonlinear

scholarly journals Positive solutions of fractional p-Laplacian equations with integral boundary value and two parameters

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Luchao Zhang ◽  
Weiguo Zhang ◽  
Xiping Liu ◽  
Mei Jia
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence Of Positive Solutions ◽  
Two Parameters ◽  
Laplacian Equations

AbstractWe consider a class of Caputo fractional p-Laplacian differential equations with integral boundary conditions which involve two parameters. By using the Avery–Peterson fixed point theorem, we obtain the existence of positive solutions for the boundary value problem. As an application, we present an example to illustrate our main result.

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