scholarly journals Positive solutions to boundary value problems of fractional difference equation with nonlocal conditions

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Shugui Kang ◽  
Yan Li ◽  
Huiqin Chen
Keyword(s):  
Difference Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Nonlocal Conditions ◽  
Fractional Difference ◽  
Fractional Difference Equation

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 On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Lili Kong ◽  
Huiqin Chen ◽  
Luping Li ◽  
Shugui Kang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Fractional Difference ◽  
Equation Boundary ◽  
Fractional Difference Equation

In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. We establish the condition of the existence of three positive solutions for this problem.

scholarly journals Positive solutions for singular discrete boundary value problems

2004 ◽  
Vol 2004 (4) ◽  
pp. 271-283 ◽  
Author(s):  
Mariella Cecchi ◽  
Zuzana Došlá ◽  
Mauro Marini
Keyword(s):  
Continuous Function ◽  
Difference Equation ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Nonlinear Difference Equation ◽  
Real Sequence ◽  
Positive Continuous Function ◽  
Positive Real ◽  
Singular Nonlinearities

We study the existence of zero-convergent solutions for the second-order nonlinear difference equationΔ(anΦp(Δxn))=g(n,xn+1), whereΦp(u)=|u|p−2u,p>1,{an}is a positive real sequence forn≥1, andgis a positive continuous function onℕ×(0,u0),0<u0≤∞. The effects of singular nonlinearities and of the forcing term are treated as well.

scholarly journals Existence of Three Positive Solutions for a Class of Boundary Value Problems of Caputo Fractional q-Difference Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Huiqin Chen ◽  
Shugui Kang ◽  
Lili Kong ◽  
Ying Gao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Green's Function ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Criteria

A class of boundary value problems of Caputo fractional q-difference equation is introduced. Green’s function and its properties for this problem are deduced. By applying these properties and the Leggett-Williams fixed-point theorem, existence criteria of three positive solutions are obtained. At last, some examples are given to illustrate the validity of our main results.

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