Existence and Uniqueness of Nontrivial Solutions for Second Order Difference Equation with Robin Boundary Value Problems

2013 ◽  
Vol 15 (2) ◽  
pp. 118
Author(s):  
Ke-yu ZHANG ◽  
Jia fa XU
Keyword(s):  
Difference Equation ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Second Order ◽  
Nontrivial Solutions ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Robin Boundary

scholarly journals Sign-variations of solutions of nonlinear discrete boundary value problems

2007 ◽  
Vol 76 (1) ◽  
pp. 33-42 ◽  
Author(s):  
Ruyun Ma
Keyword(s):  
Difference Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
The One ◽  
The Relationship

In this paper, we study two-point boundary value problems for the nonlinear second order difference equation We establish the relationship between the number of sign-variation of f on {0,…, T + 2} and the one of the solution u of the above problem.

scholarly journals Boundary Value Problem for a Second-Order Difference Equation with Resonance

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Zhenguo Wang ◽  
Zhan Zhou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Nontrivial Solutions ◽  
Order Difference ◽  
Existence And Multiplicity ◽  
Minimax Methods ◽  
Superlinear Nonlinearity ◽  
Second Order Difference Equation ◽  
Order Difference Equation

In this paper, we study the existence and multiplicity of nontrivial solutions of a second-order discrete boundary value problem with resonance and sublinear or superlinear nonlinearity. The main methods are based on the Morse theory and the minimax methods. In addition, some examples are given to illustrate our results.

scholarly journals Uniqueness and Multiplicity of Solutions for a Second-Order Discrete Boundary Value Problem with a Parameter

2008 ◽  
Vol 2008 ◽  
pp. 1-6
Author(s):  
Xi-Lan Liu ◽  
Jian-Hua Wu
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Order Difference ◽  
Multiplicity Of Solutions ◽  
Discrete Boundary Value Problem ◽  
Second Order Difference Equation ◽  
Order Difference Equation

This paper is concerned with the existence of unique and multiple solutions to the boundary value problem of a second-order difference equation with a parameter, which is a complement of the work by J. S. Yu and Z. M. Guo in 2006.

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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