What question did this study set out to answer?

Investigate the existence and positivity of multiple solutions for a class of second-order nonlinear discrete Dirichlet boundary value problems involving a general phi-Laplacian operator.

August 19, 2026The Journal of Difference Equations and Applications

Infinitely many solutions of nonlinear discrete Dirichlet boundary value problems involving ϕ -Laplacian

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Authors

WZWeimiao ZhouGuangzhou University GLGenghong LinGuangzhou University JJJuping JiGuangzhou University

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Implication

Mathematical analysis demonstrates infinite nontrivial solutions in discrete Dirichlet problems with phi-Laplacians, highlighting conditions for strictly positive states.

Key Points

Investigate the existence and positivity of multiple solutions for a class of second-order nonlinear discrete Dirichlet boundary value problems involving a general phi-Laplacian operator.
Applied variational methods and critical point theory to analyze second-order partial difference equations with Dirichlet boundary conditions.
Formulated an adapted discrete strong maximum principle to evaluate the sign and positivity of nontrivial solutions.
Established analytical conditions yielding an unbounded sequence of solutions as well as a distinct sequence of nontrivial solutions converging to zero.
Proved that all identified nontrivial solutions remain strictly positive throughout the interior of the discrete domain.

Cite This Study

Zhou et al. (2026) studied this question.

synapsesocial.com/papers/6a85638803308d306e2d6c6e https://doi.org/10.1080/10236198.2026.2714894

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Implication

Mathematical analysis demonstrates infinite nontrivial solutions in discrete Dirichlet problems with phi-Laplacians, highlighting conditions for strictly positive states.

Infinitely many solutions of nonlinear discrete Dirichlet boundary value problems involving ϕ -Laplacian

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Implication

Key Points

Cite This Study

Infinitely many solutions of nonlinear discrete Dirichlet boundary value problems involving ϕ -Laplacian

Discussion

Member takes

Implication

Key Points

Cite This Study

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