scholarly journals Solutions and Green's Functions for Boundary Value Problems of Second-Order Four-Point Functional Difference Equations

2010 ◽  
Vol 2010 (1) ◽  
pp. 973731
Author(s):  
Yang Shujie ◽  
Shi Bao
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Value ◽  
Second Order ◽  
Functional Difference ◽  
Functional Difference Equations ◽  
Order Four

Sign Properties of Green's Functions For Two Classes of Boundary Value Problems

1987 ◽  
Vol 30 (1) ◽  
pp. 28-35 ◽  
Author(s):  
P. W. Eloe
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Difference Equations ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Value ◽  
Partial Derivatives

AbstractLet G(x,s) be the Green's function for the boundary value problem y(n) = 0, Ty = 0, where Ty = 0 represents boundary conditions at two points. The signs of G(x,s) and certain of its partial derivatives with respect to x are determined for two classes of boundary value problems. The results are also carried over to analogous classes of boundary value problems for difference equations.

scholarly journals Semi-nonoscillation intervals and sign-constancy of Green’s functions of two-point impulsive boundary-value problems

2021 ◽  
Vol 73 (7) ◽  
pp. 887-901
Author(s):  
A. Domoshnitsky ◽  
Iu. Mizgireva ◽  
V. Raichik
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Impulsive Differential Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Value ◽  
Homogeneous Equation ◽  
Second Order ◽  
Differential Inequalities ◽  
Impulsive Boundary Value Problems

UDC 517.9 We consider the second order impulsive differential equation with delays    where for  In this paper, we obtain the conditions of semi-nonoscillation for the corresponding homogeneous equation on the interval   Using these results, we formulate theorems on sign-constancy of Green's functions for two-point impulsive boundary-value problems in terms of differential inequalities. 

scholarly journals On Nonlinear Boundary Value Problems for Functional Difference Equations withp-Laplacian

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Yong Wan ◽  
Yuji Liu
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Functional Difference ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value ◽  
Functional Difference Equations

Sufficient conditions for the existence of solutions of nonlinear boundary value problems for higher-order functional difference equations withp-Laplacian are established by making of continuation theorems. We allowfto be at most linear, superlinear, or sublinear in obtained results.

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