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This is a Quantitative Study study.

Multiplicity of solutions for resonant discrete 2n-th order periodic boundary value problem

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Analysis reveals multiple solutions in discrete equations through critical point theory and variational methods.

Multiple solutions have been established through critical point theory, highlighting the importance of this method.
The study demonstrates variational methods to explore periodic boundary value problems, enhancing understanding of their properties.
Two illustrative examples provided reveal key characteristics of the multiplicity of solutions in specific cases.
The findings suggest that further research can expand applications of these theoretical approaches in various contexts.

Hammouti et al. (2025) studied this question.

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