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