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A variational framework for second-order backward discrete boundary value problems

Liancheng Wang, Min Wang and James Zhang

Vol. 16 (2023), No. 1, 141–149
Abstract

We study two types of second-order discrete boundary value problems involving backward difference operators. A new variational framework is developed and used to prove the existence of solutions to the boundary value problems by critical-point theory. An example is then provided to demonstrate the application of our theoretical results.

Keywords
discrete boundary value problem, periodic boundary conditions, antiperiodic boundary conditions, variational methods, backward difference operator
Mathematical Subject Classification
Primary: 39A27
Secondary: 39A23
Milestones
Received: 9 October 2021
Revised: 8 January 2022
Accepted: 12 January 2022
Published: 14 April 2023

Communicated by Martin J. Bohner
Authors
Liancheng Wang
Department of Mathematics
Kennesaw State University
Marietta, GA
United States
Min Wang
Department of Mathematics
Kennesaw State University
Marietta, GA
United States
James Zhang
The Lawrenceville School
Lawrence Township, NJ
United States