On a solvable system of difference equations of fourth order

2013 ◽  
Vol 219 (10) ◽  
pp. 5706-5716 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Fourth Order ◽  
Difference Equations ◽  
System Of Difference Equations ◽  
Solvable System

scholarly journals ON A SOLVABLE SYSTEM OF NON-LINEAR DIFFERENCE EQUATIONS WITH VARIABLE COEFFICIENTS

2021 ◽  
Vol 21 (1) ◽  
pp. 145-162
Author(s):  
MERVE KARA ◽  
YASIN YAZLIK
Keyword(s):  
Closed Form ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Variable Coefficients ◽  
Linear Difference Equations ◽  
System Of Difference Equations ◽  
Solvable System ◽  
Initial Values ◽  
Non Linear ◽  
Forbidden Set

In this paper, we show that the system of difference equations can be solved in the closed form. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, we obtain periodic solutions of aforementioned system.

On a three-dimensional solvable system of difference equations

2020 ◽  
Vol 44 (4) ◽  
pp. 1263-1288
Author(s):  
Yacine HALIM ◽  
Massaoud BERKAL ◽  
Amira KHELIFA
Keyword(s):  
Difference Equations ◽  
Three Dimensional ◽  
System Of Difference Equations ◽  
Solvable System

scholarly journals Multiple solutions of fourth-order difference equations with different boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuhua Long ◽  
Shaohong Wang ◽  
Jiali Chen
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Difference Equations ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Sufficient Conditions ◽  
Dirichlet Boundary Conditions ◽  
Invariant Sets ◽  
Mountain Pass Lemma ◽  
Order Difference

Abstract In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

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