scholarly journals Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yansheng He ◽  
Mingzhe Sun ◽  
Chengmin Hou
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Boundary Value Problem ◽  
Multiple Positive Solutions ◽  
Order Difference ◽  
Nonlinear Boundary Value ◽  
Order Difference Equation

We consider a discrete fractional nonlinear boundary value problem in which nonlinear termfis involved with the fractional order difference. And we transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

scholarly journals Existence and Stability of the Solution of a Nonlinear Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Agneta M. Balint ◽  
Stefan Balint
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Static Stability ◽  
Nonlinear Boundary Value Problem ◽  
Existence Of A Solution ◽  
Nonlinear Boundary Value ◽  
Existence And Stability ◽  
Stability Of The Solution

The purpose is to find conditions assuring the existence of solutions for a nonlinear, boundary value problem in case of the axis-symmetric Young-Laplace differential equation. The equation describes the capillary surface between two static fluids. Necessary or sufficient conditions are found for the existence of a solution. The static stability of the obtained solution is also analyzed and stability or instability results are revealed. For the NdYAG microfiber growth, by the pulling-down method, numerical illustrations are given.

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