The Green function and correctly solvable non–local boundary value problems for the polyharmonic equation in a punctured domain

2015 ◽  
Author(s):  
Baltabek Kanguzhin ◽  
Niyaz Tokmagambetov ◽  
Nurken Bekbayev
Keyword(s):  
Green Function ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Polyharmonic Equation ◽  
Local Boundary ◽  
Non Local ◽  
The Green Function ◽  
Punctured Domain

scholarly journals Existence of Positive Solutions for Two-Point Boundary Value Problems of Nonlinear Finite Discrete Fractional Differential Equations and Its Application

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Caixia Guo ◽  
Jianmin Guo ◽  
Ying Gao ◽  
Shugui Kang
Keyword(s):  
Green Function ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Fractional Differential ◽  
The Green Function

This paper is concerned with the two-point boundary value problems of nonlinear finite discrete fractional differential equations. On one hand, we discuss some new properties of the Green function. On the other hand, by using the main properties of Green function and the Krasnoselskii fixed point theorem on cones, some sufficient conditions for the existence of at least one or two positive solutions for the boundary value problem are established.

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